Optical waveguide

ABSTRACT

An elongate waveguide for guiding light including a core having an elongate region of relatively low refractive index; a microstructured region around the core comprising elongate regions of relatively low refractive index interspersed with elongate regions of relatively high refractive index; and a boundary at the interface between the core and the microstructured region, the boundary including, in the transverse cross-section, a region of relatively high refractive index, which is connected to the microstructured region at a plurality of nodes, and at least one relatively enlarged region around the boundary, the enlarged region having a major dimension and a minor dimension, wherein the length of the major dimension divided by the length of the minor dimension is more than 3.0.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. Ser. No. 11/155,648,filed on Jun. 20, 2005, which is a continuation-in-part ofPCT-application no. PCT/GB2003/005591 filed on Dec. 22, 2003 andPCT-application no. PCT/GB2004/001288 filed on Mar. 22, 2004, and alsoclaims the priority of GB-0229826.3, GB-0302632.5, GB-0306606.5,GB-0306593.5, GB-0314485.4, GB-0321991.2, GB-0322024.1, andGB-0413843.4, the subject matter of all of the aforementionedapplications being incorporated herein in their entirety.

TECHNICAL FIELD

The present invention is in the field of optical waveguides and relatesin particular, but not exclusively, to optical waveguides that guidelight by virtue of a photonic bandgap.

BACKGROUND ART

Optical fiber waveguides, which are able to guide light by virtue of aso-called photonic bandgap (PBG), were first proposed in 1995.

In, for example, “Full 2-D photonic bandgaps in silica/air structures”,Birks et al., Electronics Letters, 26 Oct. 1995, Vol. 31, No. 22, pp.1941-1942, it was proposed that a PBG may be created in an optical fiberby providing a dielectric cladding structure, which has a refractiveindex that varies periodically between high and low index regions, and acore defect in the cladding structure in the form of a hollow core. Inthe proposed cladding structure, periodicity was provided by an array ofair holes that extended through a silica glass matrix material toprovide a PBG structure through which certain wavelengths andpropagation constants of light could not pass. It was proposed thatlight coupled into the hollow core defect would be unable to escape intothe cladding due to the PBG and, thus, the light would remain localizedin the core defect.

It was appreciated that light travelling through a hollow core defect,for example filled with air or even under vacuum, would suffersignificantly less from undesirable effects, such as non-linearity andloss, compared with light travelling through a solid silica or dopedsilica fiber core. As such, it was appreciated that a PBG fiber may findapplication as a transmission fiber to transmit light over extremelylong distances, for example across the Atlantic Ocean, withoutundergoing signal regeneration, or as a high optical power deliverywaveguide. In contrast, for standard index-guiding, single mode opticalfiber, signal regeneration is typically required approximately every 80kilometers.

The first hollow core PBG fibers that were attempted by the inventorshad a periodic cladding structure formed by a triangular array ofcircular air holes embedded in a solid silica matrix and surrounding acentral air core defect. Such fibers were formed by stacking circular orhexagonal capillary tubes, incorporating a core defect into the claddingby omitting a central capillary of the stack, and then heating anddrawing the stack, in a one or two step process, to form a fiber havingthe required structure. The first fibers made by this process had a coredefect formed by the omission of a single capillary from the center ofthe cladding structure.

U.S. Pat. No. 6,404,966 describes what is stated therein to be a PBGfiber having a hollow core region, which has an area of several timesthe optical wavelength, and a PBG cladding having a pitch equal to halfthe optical wavelength. The suggested advantage of the fiber is that itexhibits single mode behaviour.

International patent application PCT/GB00/01249 (The Secretary of Statefor Defence, UK), filed on 21 Mar. 2000, proposed the first PBG fiber tohave a so-called seven-cell core defect, surrounded by a claddingcomprising a triangular array of air holes embedded in an all-silicamatrix. The core defect was formed by omitting an inner capillary and,in addition, the six capillaries surrounding the inner capillary. Thisfiber structure appeared to guide one or two modes in the core defect,in contrast to the previous, single-cell core defect fiber, whichappeared not to support any guided modes in the core defect.

According to PCT/GB00/01249, it appeared that the single-cell coredefect fiber, by analogy to the density-of-states calculations insolid-state physics, would only support approximately 0.23 modes. Thatis, it was not surprising that the single-cell core defect fiberappeared to support no guided modes in its core defect. In contrast,based on the seven-fold increase in core defect area (increasing thecore defect radius by a factor of √7), the seven-cell core defect fiberwas predicted to support approximately 1.61 spatial modes in the coredefect. This prediction was consistent with the finding that theseven-cell core defect fiber did indeed appear to support at least oneguided mode in its core defect.

A preferred fiber in PCT/GB00/01249 was described as having a coredefect diameter of around 15 μm and an air-filling fraction (AFF)—thatis, the proportion by volume of air in the cladding—of greater than 15%and, preferably, greater than 30%. Herein, AFF (or any equivalentmeasure for air or vacuum or other materials) is intended to mean thefraction by volume of air in a microstructured, or holey, portion of thecladding, which is representative of a substantially perfect andunbounded cladding. That is, imperfect regions of the cladding, forexample near to or abutting a core defect and at an outer periphery of amicrostructured region, would not be used in calculating the AFF.Likewise, a calculation of AFF does not take into account over-claddingor jacketing layers, which may surround the microstructured region.

In “Analysis of air-guiding photonic bandgap fibers”, Optics Letters,Vol. 25, No. 2, Jan. 15, 2000, Broeng et al. provided a theoreticalanalysis of PBG fibers. For a fiber with a seven-cell core defect and acladding comprising a triangular array of near-circular holes, providingan AFF of around 70%, the structure was shown to support one or two airguided modes in the core defect. This agreed with the finding inPCT/GB00/01249.

In the book chapter entitled “Photonic Crystal Fibers: Effective Indexand Band-Gap Guidance” from the book “Photonic Crystal and LightLocalization in the 21^(st) Century”, C. M. Soukoulis (ed.), ©2001Kluwer Academic Publishers, the authors presented further analysis ofPBG fibers based primarily on a seven-cell core defect fiber. Theoptical fiber was fabricated by stacking and drawing hexagonal silicacapillary tubes. The authors suggested that a core defect must be largeenough to support at least one guided mode but that, as in conventionalfibers, increasing the core defect size would lead to the appearance ofhigher order modes. This statement appears to contradict the positionpresented in the aforementioned U.S. Pat. No. 6,404,966, whichprescribes a large core region and single mode behaviour. The authors ofthe chapter also went on to suggest that there are many parameters thatcan have a considerable influence on the performance of bandgap fibers:choice of cladding lattice, lattice spacing, index filling fraction,choice of materials, size and shape of core defect, and structuraluniformity (both in-plane and along the axis of propagation).

WO 02/075392 (Corning, Inc.) identifies a general relationship in PBGfibers between the number of so-called surface modes that exist at theboundary between the cladding and core defect of a PBG fiber and theratio of the radial size of the core defect and a pitch of the claddingstructure, where pitch is the center to center spacing of nearestneighbor holes in the triangular array of the exemplified claddingstructure. It is suggested that when the core defect boundary, togetherwith the photonic bandgap crystal pitch, are such that surface modes areexcited or supported, a large fraction of the “light power” propagatedalong the fiber is essentially not located in the core defect.Accordingly, while surface states exist, the suggestion was that thedistribution of light power is not effective to realize the benefitsassociated with the low refractive index core defect of a PBG crystaloptical waveguide. The mode energy fraction in the core defect of thePBG fiber was shown to vary with increasing ratio of core defect size topitch. In other words, it was suggested that the way to increase modeenergy fraction in the core defect is by decreasing the number ofsurface modes, in turn, by selecting an appropriate ratio of the radialsize of the core defect and a pitch of the cladding structure. Inparticular, WO 02/075392 states that, for a circular core structure, aratio of core radius to pitch of around 1.07 to 1.08 provides a highmode power fraction of not less than 0.9 and is single mode. Otherstructures are considered, for example in FIG. 7 (of WO 02/075392),wherein the core defect covers an area equivalent to 16 cladding holes.

The reason why varying the ratio of the radial size of the core defectand a pitch of the cladding structure affects the nature of the surfacemodes supported by a PBG fiber can be explained with reference to thebook “Photonic Crystals: Molding the Flow of Light”, Joannopoulos etal., Princeton University Press, ISBN 0-691-03744. The text describes indetail the nature of surface modes and, in particular, the reasons whythey form at an interface between a PBG structure and a defect (or othertermination of the PBG structure). In brief, surface modes occur whenthere are electromagnetic modes near the surface, but they are notpermitted to extend into the PBG crystal at the respective frequency dueto the PBG. The book goes on to describe that the characteristics, andindeed the presence at all, of the surface modes can be tuned by varyingthe termination position of the PBG structure. For example, a PBGstructure that terminates by cutting through air holes has differentsurface mode characteristics than the same PBG structure that terminatesby cutting through only solid material around holes. WO 02/075392 isconsistent with this since varying the core defect size of a PBG fibernaturally varies the termination position of the PBG structure.

In a Post-deadline paper presented at ECOC 2002, “Low Loss (13 dB) Aircore defect Photonic Bandgap Fiber”, N. Venkataraman et al. reported aPBG fiber having a seven-cell core defect that exhibited loss as low as13 dB/km at 1500 nm over a fiber length of one hundred meters. Thestructure of this fiber closely matches the structure considered in theaforementioned book chapter. The authors attribute the relatively smallloss of the fiber as being due to the high degree of structuraluniformity along the length of the fiber.

The present applicant's post-deadline paper presented at OFC 2004, “Lowloss (1.7 dB/km) hollow core photonic bandgap fiber”, Mangan et al,reported the lowest ever reported loss for a PBG fiber, which had anineteen cell core defect and exhibited loss below 2 dB/km at 1565 nm,and goes on to propose that scaling the fiber to operate at a longerwavelength should reduce loss even further. In conventionalstate-of-the-art solid silica fibers, attenuation is dominated byRayleigh scattering and multi-phonon absorption at short and longwavelengths, respectively, resulting in an attenuation minimum at around1550 nm. In hollow-core PBG fibers most of the light does not travel inglass, and therefore the effects of Rayleigh scattering and multi-phononabsorption in the bulk material are significantly reduced, while theinternal surfaces of the fiber become a potentially much more importantcontributor to loss. Theoretical considerations indicate that theattenuation due to mode coupling and scattering at the internalair/glass interfaces, which dominate the loss in the fiber reported,should scale with the wavelength λ as λ-3. This was confirmed by theempirical data showing the minimum loss of hollow-core PBG fibersdesigned for various operating wavelengths in a wavelength range whereIR absorption is negligible. It is likely that silica hollow-core PBGfibers will achieve their lowest loss somewhere in the 1800-2000 nmwavelength range, well beyond the wavelength at which bulk silicaassumes its minimum loss.

An alternative kind of PBG fiber, which does not have a claddingcomprising a lattice of high and low refractive index regions, isdescribed in WO00/22466. These PBG fibers typically comprise, in atransverse cross section, concentric, increasingly large, annuli ofvarying high and low refractive index material, which create anomni-directional reflector capable of confining light to a core regionof the fiber.

PBG fiber structures are typically fabricated by first forming apre-form and then heating and drawing an optical fiber from thatpre-form in a fiber-drawing tower. It is known either to form a pre-formby stacking capillaries and fusing the capillaries into the appropriateconfiguration of pre-form, or to use extrusion.

For example, in PCT/GB00/01249, identified above, a seven-cell coredefect pre-form structure was formed by omitting from a stack ofcapillaries an inner capillary and, in addition, the six capillariessurrounding the inner capillary. The capillaries around the core defectboundary in the stack were supported during formation of the pre-form byinserting truncated capillaries, which did not meet in the middle of thestack, at both ends of the capillary stack. The stack was then heated inorder to fuse the capillaries together into a pre-form suitable fordrawing into an optical fiber. Clearly, only the fiber drawn from thecentral portion of the stack, with the missing inner seven capillaries,was suitable for use as a hollow core defect fiber.

U.S. Pat. No. 6,444,133 (Corning, Inc.), describes a technique offorming a PBG fiber pre-form comprising a stack of hexagonal capillariesin which the inner capillary is missing, thus forming a core defect ofthe eventual PBG fiber structure that has flat inner surfaces. Incontrast, the holes in the capillaries are round. U.S. Pat. No.6,444,133 proposes that, by etching the entire pre-form, the flatsurfaces of the core defect dissolve away more quickly than the curvedsurfaces of the outer capillaries. The effect of etching is that theedges of the capillaries that are next to the void fully dissolve, whilethe remaining capillaries simply experience an increase inhole-diameter. Overall, the resulting pre-form has a greater fraction ofair in the cladding structure and a core defect that is closer to aseven-cell core defect than a single cell core defect.

PCT patent application number WO 02/084347 (Corning, Inc.) describes amethod of making a pre-form comprising a stack of hexagonal capillariesof which the inner capillaries are preferentially etched by exposure toan etching agent. Each capillary has a hexagonal outer boundary and acircular inner boundary. The result of the etching step is that thecenters of the edges of the hexagonal capillaries around the centralregion dissolve more quickly than the corners, thereby causing formationof a core defect. In some embodiments, the circular holes are offset inthe inner hexagonal capillaries of the stack so that each capillary hasa wall that is thinner than its opposite wall. These capillaries arearranged in the stack so that their thinner walls point towards thecenter of the structure. An etching step, in effect, preferentiallyetches the thinner walls first, thereby forming a seven-cell coredefect.

OBJECTS AND SUMMARY

The present invention deals with optical fiber waveguides that guidelight by virtue of a so-called photonic bandgap (PBG).

The optical fiber waveguides comprise a low index core (typically ahollow core) that is surrounded by a microstructured region. Between thecore and the microstructured region, the optical fiber waveguidescomprise a boundary region of high-index material.

The present invention provides improved designs of the boundary regionto reduce the total attenuation in low-index core fiber waveguides.

In at least one embodiment, the improved designs are achieved bytailored enlargements in the boundary region, where the tailoredenlargements provide anti-resonance effects that reduce the overlap ofone or more guided modes with the boundary region itself.

The anti-resonance effects result in a full or part exclusion of lightfrom the boundary region, such that a large fraction of the guided lightbecomes located in the low index regions of the fiber waveguide.

Hence, light guided in a fiber waveguide with an improved design of theboundary region according to an embodiment of the present invention hasa reduced overlap with surfaces (side-walls) of the boundary region.This reduced overlap directly reduces surface scattering of light (whichis one of the most important loss mechanism)—and thereby providesreduced total attenuation in the fiber waveguides.

In arriving at embodiments of the present invention, the inventors havedemonstrated that, while the size of a core defect is significant indetermining certain characteristics of a PBG waveguide, the form of aboundary at the interface between core and cladding also plays asignificant role in determining certain characteristics of thewaveguide. As will be described in detail hereafter, the inventors havedetermined that, for given PBG core and cladding structures, variationsin only the form of the boundary can cause significant changes in thecharacteristics of a respective waveguide.

According to a first embodiment, the present invention provides anelongate waveguide for guiding light comprising:

a core, comprising an elongate region of relatively low refractiveindex;

a microstructured region around the core comprising elongate regions ofrelatively low refractive index interspersed with elongate regions ofrelatively high refractive index; and

a boundary at the interface between the core and the microstructuredregion, the boundary comprising, in the transverse cross-section, aregion of relatively high refractive index, which is connected to themicrostructured region at a plurality of nodes, characterized by atleast one relatively enlarged region around the boundary (and excludinga boundary having twelve nodes and six enlarged regions substantially ata mid-point between six pairs of relatively more-widely-spaced apartneighboring nodes).

Alternatively, the boundary should fulfill at least one of theconditions selected from the group consisting of a) the boundary hastwelve nodes and at least one enlarged region substantially at amid-point between a pair of relatively less-widely-spaced apartneighboring nodes, or b) the boundary has less than six enlarged regionssubstantially at a mid-point between six pairs of relativelymore-widely-spaced apart neighboring nodes or more than six enlargedregions substantially at a mid-point between six pairs of relativelymore-widely-spaced apart neighboring nodes, and c) the boundary has lessthan twelve nodes or more than twelve nodes.

Or, in another alternative, if the boundary has precisely twelve nodesand six enlarged regions substantially at a mid-point between six pairsof relatively more-widely-spaced apart neighbouring nodes, the boundarycomprises at least one additional enlarged region.

As used herein, the term “relatively enlarged region” may have variousdifferent meanings depending upon the particular form of the boundary.For example, a relatively enlarged region may mean a bead-like formationor a locally thicker region along a relatively thinner boundary. Abead-like formation may be substantially oval in shape and have itsmajor axis oriented radially or azimuthally with respect to the centerof the waveguide structure. Alternatively, a relatively enlarged regionmay mean a nodule, outcrop, lump or projection, on either an inner orouter periphery of the boundary. Alternatively, a relatively enlargedregion may mean a relatively thicker region around the boundary.Embodiments of the present invention apply one or more of these kinds offeatures, as will be described hereinafter.

The boundary region is a continuous shell of relatively high refractiveindex in that it does not comprise regions of relatively low refractiveindex: all relatively-high-index regions in the boundary are connectedto each other only by relatively-high-index regions. The core is takento be contiguous with the boundary region. The core thus comprises allconnected regions of relatively low refractive index that are surroundedby the boundary region. The boundary region may be not smooth: it mayfor example be corrugated, with indented regions (for example, formed byomitting every other vein from an innermost polygon of the cladding,such as what would, if all veins were present, be an hexagon defining anhexagonal core), or it may have one two or more struts that projecttowards the center of the core (which struts may be of uniform thicknessor may have nodules at some point along their length, for example attheir ends). Thus, the core need not be of a regular cross section butmay, for example, have projections and indentations defined by theboundary region.

Thus the boundary region may be corrugated with 2, 3, 4, 5, 6, 7, 8, 9,10 or more recesses or indentations, which may be arranged at regularintervals around the center of the core.

The present invention differs from the PBG fiber structure described inthe aforementioned book chapter. That particular structure, which isillustrated in FIG. 1 in the accompanying drawings, and which isattributed with having attained the aforementioned 13 dB/km loss figure,has been discussed in numerous papers and articles since 2001. Similarto the disclosed structure, the structure of an embodiment of thepresent invention has bead-like formations 165 along consecutive longersides 140 of the boundary 145 around the core region 110. The beadlikeformations are merely an artefact and natural consequence of usinghexagonal cross section capillaries, or the process used to make thefiber, as described in further detail hereinafter with reference toFIG. 1. Even relatively recently, a similar PBG fiber structure has beenconsidered in detail in “Surface modes and loss in air-core photonicband-gap fibers”, Allan et al., Photonic Crystal Materials and Devices,Proceedings of SPIE, Volume 5000, 28-30 Jan. 2003. In that paper, theauthors provided a study of the fiber structure and attributed a certainamount of loss in the fiber as being due to mode coupling of light fromcore modes to so-called ‘surface modes’, which exist around the coreboundary. The present inventors have discovered that, according toembodiments of the present invention, it is possible to use similarbead-like formations, among many other configurations of core boundary,to tune the modal properties of a given PBG fiber. In some cases, it isbelieved that embodiments of the present invention may be used tomitigate the deleterious effects of the aforementioned mode coupling bydetuning the surface modes, either by removing them or shifting themfurther from the core modes.

Considering, for example, an air-core and silica PBG fiber, theinventors have determined that the geometry of the region of theboundary between the air core and the photonic bandgap claddingstructure has profound effects on the modal properties of the fiber. Inparticular, the inventors have appreciated that the number of guidingmodes within the band gap, the relative position of those guided modesin the modal spectrum, the fraction of the light power of the guidedmodes confined within the air core and the field intensity of thesemodes at the air-silica interfaces all vary sensitively with thegeometry within the region. In particular, the inventors have shown thatby tailoring the geometry, the properties of an LP₀₁-like mode (whenpresent), which possesses an approximately Gaussian intensity profiletowards the center of the core, can be tailored so that up to and evenover 99% of the light is confined within air, and predominantly in thecore. This implies that loss due to Rayleigh scattering in the silicamay be suppressed by up to two orders of magnitude and that nonlinearitymay be substantially reduced compared with standard index guiding singlemode fiber. Also, the inventors have demonstrated that the core boundarygeometry can be designed to reduce the field intensity of this modestrongly in the vicinity of the air-silica interfaces. This has theeffect of reducing both the small scale interface roughness scattering,which is discussed in detail hereafter, and the mode coupling due tolonger range fiber variations.

In an embodiment, the boundary region has a shape such that, in use,light guided by the waveguide is guided in a transverse mode in which,in the transverse cross-section, more than 95% of the guided light is inthe regions of relatively low refractive index in the waveguide.

According to embodiments of the invention that are describedhereinafter, there are plural enlarged regions around the boundary. The,or at least one, enlarged region may be positioned between neighboringnodes.

There may in some embodiments be six enlarged regions around theboundary, or there may be more than six enlarged regions around theboundary. For example, there may be twelve or more enlarged regionsaround the boundary.

In some embodiments, the core boundary may comprise eighteen nodes.There may be enlarged regions between six or more pairs of neighboringnodes. For example, the boundary may have enlarged regions betweentwelve pairs of neighboring nodes.

In some examples, there is only one enlarged region between any pair ofneighboring nodes. In other examples, there are plural enlarged regionsbetween at least one pair of neighboring nodes. The plural enlargedregions may be substantially equi-spaced around the boundary. Indeed,there may be plural groups of two or more enlarged regions and thegroups may be substantially equi-spaced around the boundary.

In other embodiments, the enlarged regions may not be equally spacedaround the boundary and the boundary, may have no rotational symmetry assuch, or a reduced rotational symmetry compared with the characteristicrotational symmetry of the photonic band-gap structure. In this way, theoverall structure may be rendered birefringent, for example if theenlarged regions are arranged to render the boundary two fold (or less)rotationally symmetric.

According to some embodiments, the nodes around the boundary areconnected by relatively high refractive index veins. Then, a pluralityof enlarged regions may be positioned along veins and spaced apart fromany nodes.

The boundary region may comprise a nodule. The boundary region maycomprise 2, 3, 4, 5, 6, 7, 8, 9 or more nodules, which may be arrangedat regular intervals around the center of the core. The nodules may bearranged at the centers of veins, where each vein extends between twonodes.

Alternatively, the nodules may be arranged off-center on such a vein.

In another form, an enlarged region comprises a relatively thick vein,compared to the thickness of at least one other vein, extending betweena pair of neighboring nodes.

In yet another form the boundary may comprise at least one ridgedregion, characterised by plural enlarged regions in relatively closeproximity. There may be plural ridged regions around the boundary.Indeed, a significant portion of the boundary may be ridged. In thelimit, substantially the entire boundary may be ridged. The ridges maybe on one or both peripheries of the boundary.

In some embodiments, at least one enlarged region is located on an outerperiphery of the boundary. The enlarged region may resemble an outcropor projection. In addition, or alternatively, at least one enlargedregion may be located on an inner periphery of the boundary. In somecases, there may be is at least one enlarged region on both the innerand outer peripheries of the boundary.

The microstructured region, in the plane cross section, may comprise asubstantially periodic array of relatively low refractive index regions,being separated from one another by relatively high refractive indexregions, the array having a characteristic primitive unit cell and apitch Λ. For example, the microstructured region may comprise asubstantially periodic, triangular array of relatively low refractiveindex regions. A primitive unit cell is a unit cell of the structure,having a smallest area (in the transverse cross section) that, by vectortranslations, can tile and reproduce the entire structure withoutoverlapping itself or leaving voids. The pitch Λ is the minimumtranslation distance between two neighboring primitive unit cells.

In some embodiments, the core is a seven cell defect (that is, it has aform that would result from omission or removal of relatively highrefractive index regions from a first primitive unit cell and the sixprimitive unit cells that surround the first primitive unit cell of atriangular array of unit cells.

Alternatively, the core is a nineteen cell core defect (that is, it hasa form that would result from omission or removal of relatively highrefractive index regions from a first primitive unit cell, the sixprimitive unit cells that surround the first primitive unit cell and thetwelve primitive unit cells that surround said six primitive unit cells,in a triangular array of unit cells.

Hitherto, the prior art teachings relating to PBG fibers have focused ona core defect that is just large enough to support a single mode, butnot so large that it supports additional, unwanted modes. In practice,in the prior art, the preferred core defect size for fibers that haveactually been made has generally been selected to be larger than asingle unit cell but no larger than about the size of seven inner mostcapillaries, or unit cells, in a triangular array of capillaries. U.S.Pat. No. 6,404,966 purports to describe a single mode hollow core PBGfiber. However, it is unclear from the description how it would bepossible to form a single mode PBG fiber having a large hollow coredefect, particularly if the cladding has a pitch which is only half theoptical wavelength.

As will be described herein, the present inventors have demonstratedthat increasing the core defect size beyond sizes proposed in the priorart teachings may provide significant benefits, which potentiallyoutweigh the perceived or actual disadvantages of doing so.

The present inventors also demonstrate that at least some of theperceived disadvantages of increasing the core defect size, based onwell-understood theory for index-guiding fibers, do not necessarilyapply in the case of PBG fibers. In addition, the present inventorspropose that, to the extent certain perceived disadvantages ofincreasing the core defect size do exist, there are ways to mitigatethese effects by careful design of the PBG fiber structure. A number ofpossible ways to mitigate such effects will be considered. Inparticular, the inventors demonstrate that the number and kinds of modesthat are supported by a PBG fiber are not determined only by thediameter of the core defect, an index difference between a core andcladding and wavelength of light, unlike in a conventional index-guidingfiber. Indeed, the present inventors demonstrate herein that it ispossible to increase the diameter of the core defect significantlywithout proportionately increasing the numbers of core modes supportedby the PBG fiber. In addition, the present inventors show that coremodes supported by the PBG fiber can be manipulated by varying only theform of the boundary region around the core.

The relatively low refractive index regions may be voids under vacuum orfilled with air or another gas, for example N₂ or Ar.

At least some of the relatively high refractive index regions maycomprise silica glass, for example pure or doped silica glass or othersilicate glasses, although any other inorganic glass or organic polymercould be used in any practical combination.

At least some of the boundary veins may be substantially straight.Alternatively, or in addition, at least some boundary veins may be bowedinwardly or outwardly.

The microstructured region may comprise a photonic band-gap structure.Then, at least some of the enlarged regions may deviate from the form ofthe photonic band-gap structure. For example, there may be additionalenlarged regions or the regions may be larger than would be expectedfrom inspection only of the PBG structure.

Indeed, the boundary may have a different structure from the structureof the rest of the outer structure. For example, the regions ofrelatively high refractive index in the boundary region may be thickeror thinner than corresponding regions in the rest of the outerstructure. The regions of relatively high refractive index may includenodes or nodules that are in different positions or have different sizesfrom corresponding features in the rest of the outer structure (it maybe that there are no corresponding features in the outer structure orthat there are such features in the outer structure but they are notpresent in the boundary region). The regions of relatively highrefractive index in the boundary region may include a region of adifferent refractive index from the refractive index of correspondingregion in the outer structure.

It is highly unlikely in practice that a photonic bandgap structureaccording to embodiments of the present invention will comprise a‘perfectly’ periodic array, due to imperfections being introduced intothe structure during its manufacture and/or perturbations beingintroduced into the array by virtue of the presence of the core defectand/or additional layers (over-cladding) and jacketing around thephotonic band-gap structure. The present invention is intended toencompass both perfect and imperfect structures. Likewise, any referenceto “periodic”, “lattice”, or the like herein, imports the likelihood ofimperfection.

Even if the outer structure is not a photonic bandgap structure, anyfeatures set out above in relation to other aspects of the inventionhaving a bandgap structure may be found in the present further aspect ofthe invention unless that is not physically meaningful.

In addition, core boundaries having the aforementioned (and respectivefollowing) form may be used in combination with periodic or non-periodicphotonic band-gap structures. Although periodic arrays are more commonfor forming a photonic band-gap, in principle, the array need not beperiodic—see, for example, “Antiresonant reflecting photonic crystaloptical waveguides”, by N. M. Litchinitser et al., Optics Letters,Volume 27, No. 18, Sep. 15, 2002, pp 1592-1594. Although this paper doesnot provide calculations explicitly for PBG fibers, it does illustratethat photonic bandgaps may be obtained without periodicity.

An enlarged region may be coincident with a node such that the nodeappears to have an uncharacteristic form relative to the photonicband-gap structure. Typically, nodes or the like in prior art PBG fiberstructures have a form that is substantially dictated by the form of thePBG cladding structure or the process used to make the PBG structure. Inparticular, in the prior art nodes tend to have a similar size and formas the other node-like formations in the PBG cladding structure.According to some embodiments of the present invention, however, thenodes that appear to have an uncharacteristic form may, by design, belarger, smaller or generally have a different form than the claddingnodes.

The proportion by volume of relatively low refractive index regions inthe microstructured region may be greater than 75%. For example, it mayexceed 80%, 85% or even 90%.

In preferred embodiments of the present invention, the waveguidesupports a mode in which greater than 95% of the mode power in thewaveguide is in relatively low refractive index regions. In someembodiments, more than 98% or even 99% of the mode power is in therelatively low refractive index regions.

Typically, the waveguide supports a mode having a mode profile thatclosely resembles the fundamental mode of a standard, single modeoptical fiber. This mode may support a maximum amount of the mode powerin relatively low refractive index regions compared with other modesthat are supported by the waveguide.

In addition, or alternatively, the waveguide supports a core-guided,non-degenerate mode. This mode may be the lowest loss mode of thewaveguide. Alternatively, the fundamental-like mode may be the lowestloss mode of the waveguide.

In general, at least for larger core sizes (for example seven cell coredefects and larger) the waveguide supports plural core-guided modes.

The waveguide may have an operating wavelength, wherein the pitch of themicrostructured region is greater than the operating wavelength.

According to a second embodiment, the present invention provides anoptical fiber comprising a waveguide described above as being in accordwith the present invention.

According to a third embodiment, the present invention provides atransmission line for carrying data between a transmitter and areceiver, the transmission line including along at least part of itslength a fiber of the aforementioned kind.

According to a fourth embodiment, the present invention provides apreform for a microstructured optical fiber waveguide, comprising astack of parallel, first elongate elements supported, in the plane crosssection, around an inner region, which is to become a relatively lowrefractive index core region when the preform is drawn into a fiber, thepreform further comprising second elongate elements, also supported orsituated around the inner region, said second elements being arranged togenerate a core boundary, at the interface between the photonic band-gapcladding and the core, when the preform is drawn into fiber, thearrangement of second elements being such that the core boundarycomprises at least one relatively enlarged region when the preform isdrawn into fiber.

The preform may further comprise a third elongate element for supportingthe first and second elongate elements around the inner region. Thethird elongate elements may be a solid member or it may have a bore.

At least some of the second elongate elements may be situated ininterstitial regions that form between the first elongate elements andthe third elongate element. The third elongate element may have at leastone elongate detent around its periphery and one or more of the secondelongate elements are situated in the detent or detents.

At least some second elongate elements are attached to an outerperiphery of the third elongate element. In addition, or alternatively,at least some second elongate elements are attached to an innerperiphery of the third elongate element. Second elongate elements may beattached to both inner and outer peripheries of the third elongateelement. In any case, there may be at least one second elongate elementfused to the third elongate element.

In some embodiments, the third elongate element is pre-profiled, in thetransverse cross section, to have around its periphery enlarged regionsthat constitute the second elongate elements.

In alternative embodiments, the third elongate element comprises aninner capillary within the bore of an inside an outer capillary, and atleast some second elongate elements are situated in a region that isformed between the inner capillary and the outer capillary.

In preferred embodiments, said first elongate elements are arranged, ona macro scale, to become a photonic band-gap cladding structure when thepreform is drawn into a fiber. Then, the arrangement of second elongateelements may deviate from the arrangement of first elongate elementsrequired to form the photonic band-gap cladding structure.

At least some of the second elongate elements may comprise solid rods.In addition, or alternatively, at least some of the second elongateelements may comprise capillaries. In some embodiments, the rods and/orcapillaries may be the same size. In other embodiments, the rods and/orcapillaries may be different sizes.

At least some of the first elements may have a circular cross section.At least some of the circular first elements may be capillaries. Then,said capillaries may be arranged in a triangular array. In addition,other first elongate elements may be solid rods that are situated ininterstitial regions between the capillaries.

According to a further embodiment, the present invention provides anoptical fiber made from a preform as described hereinbefore as being inaccord with the present invention.

According to a further embodiment, the present invention provides amethod of forming a photonic band-gap fiber, comprising the steps offorming a preform as described hereinbefore as being in accord with thepresent invention, and heating and drawing the preform, in one or morestages, into the fiber.

The present invention is concerned in particular with relativelyenlarged regions that are intended to be optimised in size, shape and/orlocation, to provide improved optical fiber properties.

According to an embodiment, the present invention provides an elongatewaveguide for guiding light comprising:

a core, comprising an elongate region of relatively low refractiveindex;

a microstructured region around the core comprising elongate regions ofrelatively low refractive index interspersed with elongate regions ofrelatively high refractive index; and

a boundary at the interface between the core and the microstructuredregion, the boundary comprising, in the transverse cross-section, aregion of relatively high refractive index, which is connected to themicrostructured region at a plurality of nodes, characterized by atleast one relatively enlarged region around the boundary, having a majordimension and a minor dimension, the ratio of the length of the majordimension to the length of the minor dimension (i.e. the length of themajor dimension divided by length of the minor dimension) being morethan 3.0.

As used herein, the term “relatively enlarged region” may have variousdifferent meanings depending upon the particular form of the boundary.For example, a relatively enlarged region may mean a nodule-like, orbead-like, formation or a locally thicker region along a relativelythinner boundary.

The boundary region is a continuous region of relatively high refractiveindex in that it does not comprise regions of relatively low refractiveindex: all relatively-high-index regions in the boundary are connectedto each other only by relatively-high-index regions. The core is takento be contiguous with the boundary region. The core thus comprises allconnected regions of relatively low refractive index that are surroundedby the boundary region.

In an embodiment, the boundary region has a shape such that, in use,light guided by the waveguide is guided in a transverse mode in which,in the transverse cross-section, more than 95% of the guided light is inthe regions of relatively low refractive index in the waveguide.

In some embodiments, the ratio is even larger, for example the ratio maybe more than 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0 or more than 7.5.The ratio may be larger still. For example, the ratio may be more than8.0, more than 8.5, or even as high as 9.0, or even higher.

While the present inventors have previously identified that providingenlarged regions around the core boundary can provide beneficialproperties in waveguides, for example, increased confinement of light tothe core and decreased interaction between light and relatively highrefractive index regions, the inventors have now in additiondemonstrated that the particular size, shape and location of theenlarged regions can be sensitively tuned to further-enhance thesepreviously-identified beneficial properties.

The relatively enlarged region may be located between two adjacentnodes. Alternatively, the relatively enlarged region may embody at leastone node, in which case the relatively enlarged region would be locatedbetween two, non-adjacent nodes.

The relatively enlarged region may be spaced from each neighboring nodeby a relatively narrow region, which is narrower than the minordimension and narrower than the diameter of the largest inscribed circleof the adjacent node. While nodes as such are typically not perfectlyround in cross section, the present inventors typically characterizenodes by the size of the largest inscribed circle that fits within therelatively high refractive index material that forms the node.

Preferably, the length of the major dimension is at least 0.42 times thedistance between the two adjacent nodes on either side of the enlargedregion. The distance between the nodes may be measured between nodecenters, for example defined by the center of the largest inscribedcircle of the node. The length of the major dimension may be more than0.45, more than 0.5, more than 0.6, more than 0.7, or even more than 0.8times the distance between the two adjacent nodes. According to oneexemplary embodiment, the major dimension is about 0.9 times thedistance between the two adjacent nodes on either side of the enlargedregion.

In addition, the major dimension may be less than 0.98 times or lessthan 0.95 times the distance between the two adjacent nodes.

While the prior art, for example the aforementioned N. Venkataraman etal. paper and the book chapter, have described waveguide structures thatinclude bead-like formations around a core boundary region, no prior artknown to the present inventors has attributed any significance to them.Even relatively recently, a similar fiber structure has been consideredin detail in “Surface modes and loss in air-core photonic band-gapfibers”, Allan et al., Photonic Crystal Materials and Devices,Proceedings of SPIE, Volume 5000, 28-30 Jan. 2003. In that paper, theauthors provided an in depth study of the fiber structure and attributeda certain amount of loss in the fiber as being due to mode coupling oflight from core modes to so-called ‘surface modes’, which exist aroundthe core boundary. Again, the paper made no mention of the bead-likeformations being significant in any way. In contrast, the presentinventors have discovered that, according to embodiments of the presentinvention, it is possible to use similar bead-like formations to tunethe modal properties of a given fiber. In some cases, it is believedthat embodiments of the present invention may be used to mitigate thedeleterious effects of the aforementioned mode coupling by de-tuning thesurface modes, either by removing them or shifting them further from thecore modes.

Considering, for example, an air-core and silica PBG fiber, theinventors have appreciated that the number of guiding modes within theband gap, the relative position of those guided modes in the modalspectrum, the fraction of the light power of the guided modes confinedwithin the air core and the field intensity of these modes at theair-silica interfaces all vary sensitively with the geometry within theregion. In particular, the inventors have shown that by tailoring thegeometry, the properties of an LP₀₁-like mode (when present), whichpossesses an approximately Gaussian intensity profile towards the centerof the core, can be tailored so that up to and even over 99% of thelight is confined within air, and predominantly in the core. Thisimplies that loss due to Rayleigh scattering in the silica may besuppressed by up to two orders of magnitude and that nonlinearity may besubstantially reduced compared with standard index guiding single modefiber. Also, the inventors have demonstrated that the core boundarygeometry can be designed to reduce the field intensity of this modestrongly in the vicinity of the air-silica interfaces. This has theeffect of reducing both the small scale interface roughness scattering,which is discussed in detail hereafter, and the mode coupling due tolonger range fiber variations.

In a study by the present inventors, the relatively enlarged regions inthe aforementioned prior art have typically had a majordimension—aligned azimuthally around the boundary—that is in the rangeof 0.3 to 0.4 times the distance between respective adjacent nodes.These enlarged regions have been generally oval in shape and six innumber around a core boundary comprising twelve nodes (defining aseven-cell core defect), have occurred between every other pair of nodesaround the boundary and have had an aspect ratio (major dimension lengthdivided by minor dimension length) of between two and three.

According to embodiments of the present in invention, themicrostructured region may have a characteristic pitch. In this case,the major dimension may be at least 0.42 times the characteristic pitch.The major dimension may be at least 0.45, 0.5, 0.6, 0.7, or even 0.8times the characteristic pitch. According to one exemplary embodiment,the major dimension is about 0.9 times the characteristic pitch.

In addition, the major dimension may be less than 0.98 times or lessthan 0.95 times the characteristic pitch.

The microstructured region, in the plane cross section, may comprise asubstantially periodic array of relatively low refractive index regions,being separated from one another by relatively high refractive indexregions, the array having a characteristic primitive unit cell and apitch Λ. For example, the microstructured region may comprise asubstantially periodic, triangular array of relatively low refractiveindex regions. A primitive unit cell is a unit cell of the structure,having a smallest area (in the transverse cross section) that, by vectortranslations, can tile and reproduce the entire structure withoutoverlapping itself or leaving voids. The pitch Λ is the minimumtranslation distance between two neighboring primitive unit cells.

It is highly unlikely in practice that a waveguide structure accordingto embodiments of the present invention will comprise a ‘perfectly’periodic array, due to imperfections being introduced into the structureduring its manufacture and/or perturbations being introduced into thearray by virtue of the presence of the core defect and/or additionallayers (over-cladding) and jacketing around the photonic band-gapstructure. The present invention is intended to encompass both perfectand imperfect structures. Likewise, any reference to “periodic”,“lattice”, or the like herein, imports the likelihood of imperfection.

The boundary may have a distinct form compared with other regions of thewaveguide. For example, the regions of relatively high refractive indexin the boundary region may be thicker or thinner than similar regions inthe rest of the outer structure. The regions of relatively highrefractive index may include nodes or nodules that are in differentpositions or have different sizes from corresponding features in therest of the outer structure (it may be that there are no correspondingfeatures in the outer structure or that there are such features in theouter structure but they are not present in the boundary region). Theregions of relatively high refractive index in the boundary region mayinclude a region of a different refractive index from the refractiveindex of corresponding region in the outer structure.

In some embodiments, the core is a seven cell defect (that is, it has aform that would result from omission or removal of relatively highrefractive index regions from a first primitive unit cell and the sixprimitive unit cells that surround the first primitive unit cell of atriangular array of unit cells.

Alternatively, the core is a nineteen cell core defect (that is, it hasa form that would result from omission or removal of relatively highrefractive index regions from a seven cell defect and, in addition, thetwelve primitive unit cells that surround said seven cell defect.

Hitherto, the prior art teachings relating to PBG fibers have focused ona core defect that is just large enough to support a single mode, butnot so large that it supports additional, unwanted modes. In practice,in the prior art, the preferred core defect size for fibers that haveactually been made has generally been selected to be larger than asingle unit cell but no larger than about the size of seven inner mostcapillaries, or unit cells, in a triangular array of capillaries. U.S.Pat. No. 6,404,966 purports to describe a single mode hollow core PBGfiber. However, it is unclear from the description how it would bepossible to form a single mode PBG fiber having a large hollow coredefect, particularly if the cladding has a pitch which is only half theoptical wavelength.

The present inventors have appreciated that increasing the core defectsize beyond sizes proposed in the prior art teachings may providesignificant benefits, which potentially outweigh the perceived or actualdisadvantages of doing so.

The present inventors have also appreciated that at least some of theperceived disadvantages of increasing the core defect size, based onwell-understood theory for index-guiding fibers, do not necessarilyapply in the case of PBG fibers. In addition, the present inventorspropose that, to the extent certain perceived disadvantages ofincreasing the core defect size do exist, there are ways to mitigatethese effects by careful design of the PBG fiber structure. Inparticular, the inventors demonstrate that the number and kinds of modesthat are supported by a PBG fiber are not determined only by thediameter of the core defect, an index difference between a core andcladding and wavelength of light, unlike in a conventional index-guidingfiber. The present inventors show that core modes supported by the PBGfiber can be manipulated by varying only the form of the boundary regionaround the core.

The enlarged region may have a generally oval shape.

The minor dimension may extend substantially radially with respect tothe center of the waveguide.

There may be six, or more than six, enlarged regions around theboundary. For example there may be twelve or more enlarged regionsaround the boundary.

In any event, the core boundary may comprise eighteen nodes.

In addition, or alternatively, there may be enlarged regions between sixor more pairs of neighboring nodes. For instance, the boundary may haveenlarged regions between twelve pairs of neighboring nodes.

There may be only one enlarged region between any pair of neighboringnodes.

Preferably, there are plural enlarged regions that are substantiallyequi-spaced around the boundary.

Alternatively, here may be plural groups of two or more enlarged regionsand the groups may be substantially equi-spaced around the boundary.

In some embodiments, the enlarged regions may not be equally spacedaround the boundary and the boundary may have no rotational symmetry assuch. The boundary may have no more than two fold rotational symmetryabout any longitudinal axis thereof at least in part by virtue of thepresence or placement of the or each relatively enlarged region. Forexample, the boundary may only have two fold rotational symmetry. Inthis way, the overall structure may be rendered birefringent

The relatively high refractive index regions may substantially comprisea solid matrix material, which defines a microstructure of relativelylow refractive index regions substantially comprising voids. The voidsmay be filled with a gaseous medium, for example air, N₂ or Ar, orliquid medium, or are substantially under a vacuum.

At least some of the relatively high refractive index regions maycomprise silica glass, for example pure or doped silica glass or othersilicate glasses, although any other inorganic glass or organic polymercould be used in any practical combination.

In particularly preferred embodiments of the present invention, themicrostructured region around the core is substantially arranged to forma photonic band-gap for a predetermined wavelength of light. Thephotonic band-gap may not be the only confinement mechanism in operationin the waveguide, in use.

Even if the microstructured region does not provide a photonic bandgap,any features set out above in relation to other aspects of the inventionhaving a bandgap structure may be found in the present further aspect ofthe invention unless that is not physically meaningful.

Core boundaries having the aforementioned (and respective following)form may be used in combination with periodic or non-periodic photonicband-gap structures. Although periodic arrays are more common forforming a photonic band-gap, in principle, the array need not beperiodic—see, for example, “Antiresonant reflecting photonic crystaloptical waveguides”, by N. M. Litchinitser et al., Optics Letters,Volume 27, No. 18, Sep. 15, 2002, pp. 1592-1594. Although this paperdoes not provide calculations explicitly for PBG fibers, it doesillustrate that photonic bandgaps may be obtained without periodicity.

An enlarged region may be coincident with a node such that the nodeappears to have an uncharacteristic form relative to the photonicband-gap structure. Typically, nodes or the like in prior art PBG fiberstructures have a form that is substantially dictated by the form of thePBG cladding structure or the process used to make the PBG structure. Inparticular, in the prior art nodes tend to have a similar size and formas the other node-like formations in the PBG cladding structure.According to some embodiments of the present invention, however, thenodes that appear to have an uncharacteristic form may, by design, belarger, smaller or generally have a different form than the claddingnodes.

The proportion by volume of relatively low refractive index regions inthe microstructured region may be greater than 75%. Indeed, theproportion may be greater than 80, greater than 85, greater than 90, oreven greater than 92%.

The waveguide may support a mode in which greater than 95%, greater than97%, greater than 98%, or greater than 99% of the mode power in thewaveguide is in relatively low refractive index regions.

The waveguide may support a mode having a mode profile that closelyresembles the fundamental mode of a standard, single mode optical fiber.

The aforementioned mode may support a maximum amount of the mode powerin relatively low refractive index regions compared with other modesthat are supported by the waveguide.

The waveguide may support a core-guided, non-degenerate mode. That modemay be the lowest loss mode of the waveguide.

In general, the waveguide may support plural core-guided modes.Alternatively, the waveguide may support only one core-guided mode.

The waveguide may have an operating wavelength, wherein the pitch of themicrostructured region is greater than the operating wavelength.

According to a further embodiment, the present invention provides anelongate waveguide for guiding light comprising:

a core, comprising an elongate region of relatively low refractiveindex;

a microstructured region around the core comprising elongate regions ofrelatively low refractive index interspersed with elongate regions ofrelatively high refractive index; and

a boundary at the interface between the core and the microstructuredregion, the boundary comprising, in the transverse cross-section, aregion of relatively high refractive index, which is connected to themicrostructured region at a plurality of nodes, characterized by atleast one relatively enlarged region positioned between two adjacentnodes, the relatively enlarged region having a major dimension and aminor dimension, the length of the major dimension being greater than0.42 times, and less than 0.98 times, the distance between the twoadjacent nodes.

There may be six generally similar relatively enlarged regions aroundthe boundary. Indeed, the waveguide may have any, some or all of thefeatures described in relation to another aspect of the presentinvention.

According to a further embodiment, the present invention provides anoptical fiber comprising a waveguide as hereinbefore described.

According to a further embodiment, the present invention provides atransmission line for carrying data between a transmitter and areceiver, the transmission line including the aforementioned fiber alongat least part of its length.

An object of the present invention is to provide a PBG waveguide havingimproved properties, in particular lower loss, than prior art PBGwaveguides.

In arriving at the present invention, the inventors have demonstratedthat, while the size of a core defect is significant in determiningcertain characteristics of a PBG waveguide, the form of a boundary atthe interface between core and cladding also plays a significant role indetermining certain characteristics of the waveguide. As will bedescribed in detail hereafter, the inventors have determined that, forgiven PBG core and cladding structures, variations in only the form ofthe boundary can cause significant changes in the characteristics of arespective waveguide.

According to an embodiment of the invention there is provided anelongate waveguide for guiding light comprising: a core, comprising anelongate region of relatively low refractive index; and amicrostructured region comprising a photonic bandgap structure arrangedto provide a photonic bandgap over a range of wavelengths of light, thestructure comprising elongate regions of relatively low refractive indexinterspersed with elongate regions of relatively high refractive index,including a boundary region of relatively high refractive index thatsurrounds, in a transverse cross-section of the waveguide, the core;characterized in that the boundary region has a shape such that, in use,light guided by the waveguide is guided in a transverse mode in which,in the transverse cross-section, more than 95% of the guided light is inthe regions of relatively low refractive index in the waveguide.

In referring to the ‘shape’ of the boundary region, we mean ‘shape’ in abroad sense, both its gross shape (whether it is for example circular orhexagonal or dodecagonal or some other shape) and fine details of itsshape, for example the presence or absence of local variations inthickness (for example, nodes or nodules) around its perimeter. (It isexpected that the gross shape of the boundary will generally define theshape of the core.) We also use the word ‘shape’ to encompass the sizeof the boundary region; for example, we regard a boundary region that isa circular shell in the transverse plane to have a different shape for adifferent diameter of the shell or for a different thickness of theshell, even though it remains a circular shell in each of those cases.

The regions of relatively low refractive index in the waveguide ofcourse comprise the regions of relatively low refractive index in thephotonic bandgap structure and the region of relatively low refractiveindex in the core.

The regions of relatively low refractive index may have a refractiveindex of less than 2, less than 1.8, less than 1.6, less than 1.5, lessthan the refractive index of silica, less than 1.4, less than 1.3, lessthan the refractive index of typical polymer glasses (for example, lessthan 1.25), less than 1.2 or even less than 1.1 or even less than 1.05,or be 1 for the case of a vacuum.

The inventors have discovered that in considering how best to lower lossin an optical waveguide having a photonic bandgap cladding structure, itis helpful to consider the behaviour of distinct features in thecladding boundary as being that of optical resonators.

Considering, for example, an air-core and silica PBG fiber, theinventors have determined that the geometry of the region of theboundary between the air core and the photonic bandgap claddingstructure has profound effects on the modal properties of the fiber. Inparticular, the inventors have appreciated that the number of guidingmodes within the band gap, the fraction of the light power of the guidedmodes confined within the air core and the field intensity of thesemodes at the air-silica interfaces all vary sensitively with thegeometry within the region. In particular, the inventors have shown thatby tailoring the geometry, the properties of an LP01-like mode (whenpresent), which possesses an approximately Gaussian intensity profiletowards the center of the core, can be tailored so that up to and evenover 99% of the light is confined within air, and predominantly in thecore. This implies that loss due to Rayleigh scattering in the silicamay be suppressed by up to two orders of magnitude and that nonlinearitymay be substantially reduced compared with standard index guiding singlemode fiber. Also, the inventors have demonstrated that the core boundarygeometry can be designed to reduce the field intensity of this modestrongly in the vicinity of the air-silica interfaces. This has theeffect of reducing both the small scale interface roughness scattering,which is discussed in detail hereafter, and the mode coupling due tolonger range fiber variations.

The inventors have determined that the design of a core-claddinginterface, or boundary region, can exploit an anti-resonance effect tostrongly enhance the power in air fraction, η, and reduce the fieldintensity at the air-silica interfaces of core-guided modes, such as theLP01-like mode. Antiresonant boundaries have also been found, in atleast some embodiments, to have the benefit of reducing the effects of,or even removing, so-called surface modes that can exist at a coreboundary and potentially interfere with the core-guided modes. This isparticularly surprising given that an antiresonant core boundary doesnot typically match the form of the cladding.

A simple example of an optical resonator is the Fabry-Perotinterferometer. Whether or not light can resonate in such a featuredepends on the feature's size, shape and composition, and also on thewavelength and direction of propagation of the light. As the wavelengthis varied the feature moves into and out of resonance.

Such antiresonant effects can be observed in slab-like resonators,having plane parallel faces between which light is reflected andinterferes destructively at antiresonance. The effect can also beobserved in a ring-like resonator, where interference is betweenreflectors from an outer and an inner shell surface. It has beenreported by Litchinitser et al., Opt. Lett., Vol. 27 (2002) pp.1592-1594, that light may be guided in a PBG-like fiber predominantly byanti-resonant reflection in multiple cladding layers. Litchinitser etal. describe a fiber structure comprising a low index core surrounded byplural concentric layers of high and low index material, the relativethickness of which were chosen to provide an anti-resonant claddingstructure for confining light to the core region.

Litchinitser also mentions a PCF consisting of a silica core surroundedby holes filled with high index liquid. In that case the silicarepresents the low index medium and the filled holes are the featuresthat act as resonators. At their antiresonant wavelengths, the filledholes substantially exclude light and thus confine light to therelatively low-index silica core. The present inventors have consideredmore complicated structures, which may, for example, comprise high-indexfeatures interconnected by high index “struts”, whereas the resonatorsdescribed by Litchinitser et al. are isolated cylinders. Neverthelessthe present inventors have discovered that such interconnected featurescan act as distinct resonators, and serve to confine light in the lowindex medium (for example, air) when they are antiresonant.

For a given excitation, on resonance, the optical power in the featuresassumes a maximum. In between resonances, optical power in the featuresis minimised. In a photonic crystal fiber, if the relatively lowrefractive index regions are air, it is desirable to maximise the amountof light in these regions in order to reduce scattering, non-linearitiesand other deleterious effects. Hence it is advantageous to incorporatefeatures that possess strong distinct resonances, and adjust their sizesand shapes so that they are antiresonant at the optical wavelengths anddirections of propagation of interest.

That is advantageous as it raises the proportion of light in low-indexregions and decreases F-factor (defined below), which is a measure ofthe amount of light at glass/air interfaces.

The present inventors have discovered that confinement of light to acore of a PBG fiber, which confines light to the core region by virtueof a photonic bandgap, may be enhanced by providing, at the interfacebetween the core and the photonic bandgap cladding, a boundary which istuned to be substantially anti-resonant. Unlike in Litchinitser et al.,in which antiresonance is achieved using concentric layers of materialor distinct, unconnected resonators, a core boundary proposed herein maycomprise plural anti-resonant features around an unbroken, but otherwisegenerally non-antiresonant, core boundary. The present inventors havediscovered that such a core boundary can be arranged to be antiresonantat an operating wavelength, and thereby serve to confine light to thecore of the waveguide. The present inventors have also discovered thatit is possible to achieve a similar confinement of light to a core byarranging a single, unbroken region of relatively high refractive indexat the interface between the core and the photonic bandgap structure.This latter kind of confinement, while being closely related to theformer kind, is described more fully in applicant's co-pendingInternational Patent Application, having the title “Enhanced OpticalWaveguide”, filed on the same date and having the same earliest prioritydate as this application (the entire contents of the co-pendingapplication is hereby incorporated herein by reference).

As discussed above, guiding light in a region of relatively lowrefractive index has the advantage that losses, nonlinear effects andother material effects are generally lower in such regions, particularlyif the region is a region of air or a gas. Thus preferably, ever more ofthe light is guided in the regions of relatively low refractive index inthe PBG structure or in the region of relatively low refractive index inthe core: preferably more than 96%, more than 97%, more than 98%, morethan 99%, more than 99.3%, more than 99.5% or even more than 99.9% ofthe light is in those regions.

The boundary region may have a shape such that, in use, light guided bythe waveguide is guided in a transverse mode in which, in the transversecross-section, more than 50% of the guided light is in the region ofrelatively low refractive index in the core. It is significant that theinventors have recognised that the light need not be in the core regionfor beneficial effects to be achieved. Thus, the boundary region mayhave a shape such that, in use, light guided by the waveguide is guidedin a transverse mode in which, in the transverse cross-section, morethan 1% of the guided light is in the regions of relatively lowrefractive index in the photonic bandgap structure. It may be that stillmore of the guided light is in those regions in the PBG structure: morethan 2%, more than 5% or even more than 10% of the light may be in thoseregions.

F-factor has been identified by the present inventors as a useful figureof merit which relates to how the guided light propagating in a PBGfiber is subject to scattering from small scale irregularities of theair-silica interfaces. F-factor is also believed to be a strongindicator of likely mode-coupling characteristics of a PBG-fiber.

The guided light propagating in a PBG waveguide is subject to scatteringfrom small scale irregularities of the interfaces between higherrefractive index regions and lower refractive index regions. That lossmechanism acts in addition to the Rayleigh scattering due to indexinhomogeneity within the higher index regions. The latter loss mechanismis strongly suppressed in PBG waveguides having for example an air core,since most of the light power resides in air. The amount of scatteringassociated with the interfaces can be minimised by ensuring thatimpurities are eliminated during the draw process; such impurities canact as scattering (and absorption) centers directly, and can operate asnucleation sites for crystallite formation. With such imperfectionsremoved, there still remains interface roughness governed by thethermodynamics of the drawing process. Such fluctuations are likely tobe difficult or impossible to remove.

The Rayleigh scattering due to small scale roughness at thelower-index/higher-index (e.g. air-silica) interfaces can be calculatedby applying a perturbation calculation. The analysis has a simpleinterpretation in terms of effective particulate scatterers distributedon the interfaces. If the root-mean square (RMS) height roughness ish_(rms) and the correlation lengths of the roughness along the holedirection and around the hole perimeter are L_(z) and L_(φ)respectively, then a typical scatterer has a volume h_(rms)L_(z)L_(φ).The induced dipole moment of the typical scatterer is then given by

p=Δ∈E₀h_(rms)L_(z)L_(φ),  (1)

where Δ∈ is the difference in dielectric constant between thehigher-index and the lower-index regions, and E₀ is the E-field strengthat the scatterer. That induced dipole moment radiates a power, in thefree space approximation, given by

$\begin{matrix}\begin{matrix}{P_{sc} = {\frac{1}{12\; \pi}( \frac{\omega}{c} )^{4}( \frac{ɛ_{0}}{\mu_{0}} )^{1/2}{p}^{2}}} \\{= {\frac{1}{12\; \pi}( \frac{\omega}{c} )^{4}\Delta \; ɛ^{2}h_{rms}^{2}L_{z}^{2}{L_{\varphi}^{2}( \frac{ɛ_{0}}{\mu_{0}} )}^{1/2}{{E_{0}}^{2}.}}}\end{matrix} & (2)\end{matrix}$

The number density of particles on the interface will be ˜1/(L_(z)L_(φ))so that the total radiated power from a section of length L of theperturbed fiber will be approximately

$\begin{matrix}{P_{rad} \sim {\frac{1}{12\; \pi}( \frac{\omega}{c} )^{4}\Delta \; ɛ^{2}h_{rms}^{2}L_{z}L_{\varphi}{L( \frac{ɛ_{0}}{\mu_{0}} )}^{1/2}{\oint\limits_{{hole}\mspace{14mu} {perimeters}}{{s}{E_{0}}^{2}}}}} & (3)\end{matrix}$

The loss rate is thus given by

$\begin{matrix}{\gamma = {\frac{P_{rad}}{P_{0}L} \sim {\frac{1}{6\; \pi}( \frac{\omega}{c} )^{4}\Delta \; ɛ^{2}h_{rms}^{2}L_{z}{L_{\varphi}( \frac{ɛ_{0}}{\mu_{0}} )}^{1/2}\frac{\oint\limits_{{hole}\mspace{14mu} {perimeters}}{{s}{E_{0}}^{2}}}{\int{{{S( {E_{0}\bigwedge H_{0}^{*}} )}} \cdot \hat{z}}}}}} & (4)\end{matrix}$

where the incident power P₀ has been expressed as a Poynting flux.

Equation (4) shows that the mode shape dependence of the Rayleighinterface roughness scattering strength is governed by a factor F givenby

$\begin{matrix}{F = {( \frac{ɛ_{0}}{\mu_{0}} )^{1/2}{\frac{\oint\limits_{{hole}\mspace{14mu} {perimeters}}{{s}{{E_{0}( r^{\prime} )}}^{2}}}{\int_{x\text{-}{section}}\ {{{S( {E_{0}\bigwedge H_{0}^{*}} )}} \cdot \hat{z}}}.}}} & (5)\end{matrix}$

A comparison of the interface scattering strength from guided modes ofdifferent fibers with similar interface roughness properties can bebased purely on this factor. Indeed, the thermodynamic limit to surfaceroughness is not expected to vary significantly with the details of thefiber geometry, so that the factor F can be used directly as a figure ofmerit.

A more rigorous calculation of small scale interface roughness can bederived which takes into account the details on the surface roughnessspectrum and deviations from the free space approximation. The lattereffect is embodied by a local density of states (LDOS) correction factorappearing in the integrand of the numerator integral in equation (5).Ideally, to minimise the interface loss, the field intensity of theguiding mode multiplied by the LDOS factor should be maintained as smallas possible at the interfaces. In practise, the LDOS correction is foundto be small even for (silica/air) band gap fibers in comparison with theguided mode field intensity factor, so that the factor F given inexpression (5) may be used to compare the interface scattering strengthfrom guided modes of different fiber designs.

The effect of the scattering from crystallites which have formed closeto the air/silica interfaces can be calculated in a similar way to thegeometrical roughness considered above. Assuming the number density perunit interface length and the size of the crystallites is independent offiber design, again F can be used directly to compare the interfacescattering strengths.

The boundary region may have a shape such that, in use, light guided bythe waveguide is guided in a transverse mode providing an F-factor ofless than 0.23 μm⁻¹. That figure is calculated assuming that thewaveguide guides light at a frequency of 1.55 μm. For the case in whichthe Photonic Band Gap structure is a periodic structure having a pitchΛ, the F-factor is preferably less than 0.7 Λ⁻¹.

Also according to an embodiment of the invention there is provided anelongate waveguide for guiding light comprising:

a core, comprising an elongate region of relatively low refractiveindex; and

a photonic bandgap structure arranged to provide a photonic bandgap overa range of frequencies of light, the structure comprising elongateregions of relatively low refractive index interspersed with elongateregions of relatively high refractive index, including a boundary regionof relatively high refractive index that surrounds, in a transversecross-section of the waveguide, the core;

characterized in that the boundary region has a shape such that, in use,light guided by the waveguide is guided in a transverse mode providingan F-factor of less than 0.23 μm⁻¹ (or, for a waveguide in which thePhotonic Band Gap structure is a periodic structure having a pitch Λ,0.7Λ⁻¹).

Preferably, still lower F-factors are provided: less than 0.192 μm⁻¹ (or0.6Λ⁻¹ if periodic), less than 0.16 μm⁻¹ (or 0.5Λ⁻¹ if periodic), lessthan 0.128 μm⁻¹ (or 0.4Λ⁻¹ if periodic), less than 0.10 μm⁻¹ (or 0.3Λ⁻¹if periodic), less than 0.080 μm⁻¹ (or 0.25Λ⁻¹ if periodic), less than0.065 μm⁻¹ (or 0.2Λ⁻¹ if periodic), less than 0.060 μm⁻¹ (or 0.188Λ⁻¹ ifperiodic), less than 0.055 μm⁻¹ (or 0.17Λ⁻¹ if periodic), less than0.052 μm⁻¹ (or 0.163Λ⁻¹ if periodic), less than 0.048 μm⁻¹ (or 0.15Λ⁻¹if periodic), less than 0.04 μm⁻¹ (or 0.125Λ⁻¹ if periodic), less than0.032 μm⁻¹ (or 0.10Λ⁻¹ if periodic), less than 0.029 μm⁻¹ (or 0.090Λ⁻¹if periodic), less than 0.026 μm⁻¹ (or 0.080Λ⁻¹ if periodic), less than0.022 μm⁻¹ (or 0.070Λ⁻¹ if periodic), less than 0.02 μm⁻¹ (or 0.063Λ⁻¹if periodic), less than 0.019 μm⁻¹ (or 0.060Λ⁻¹ if periodic), less than0.016 μm⁻¹ (or 0.05Λ⁻¹ if periodic), less than 0.013 μm⁻¹ (or 0.040Λ⁻¹if periodic), less than 0.012 μm (or 0.038Λ⁻¹ if periodic), 0.010 μm⁻¹(or 0.030Λ⁻¹ if periodic), less than 0.006 μm⁻¹ (or 0.020Λ⁻¹ ifperiodic), or even less than 0.003 μm⁻¹ (or 0.010Λ¹ if periodic) arepreferred.

The relevant F-factor is typically the F-factor only of the mode ofinterest (for example, the fundamental mode, ignoring higher-ordermodes).

The features next discussed may be found in embodiments of either aspectof the invention (relating to high levels of light in the relatively lowrefractive index regions or relating to F-factor).

In the transverse cross section, the photonic bandgap structure maycomprise an array of the relatively low refractive index regionsseparated from one another by the relatively high refractive indexregions. The array may be substantially periodic. (However, inprinciple, the array need not be periodic—see, for example, the paper byN. M. Litchinitser et al. discussed above. Although that paper does notprovide calculations explicitly for PBG fibers, it does illustrate thatphotonic bandgaps may be obtained without periodicity.)

It is highly unlikely in practice that a photonic bandgap structureaccording to the present invention will comprise a ‘perfectly’ periodicarray, due to imperfections being introduced into the structure duringits manufacture and/or perturbations being introduced into the array byvirtue of the presence of the core defect. The present invention isintended to encompass both perfect and imperfect structures. Likewise,any reference to “periodic”, “lattice”, or the like herein, imports thelikelihood of imperfection.

The array may be a substantially triangular array. Other arrays, ofcourse, may be used, for example, square, hexagonal or Kagome, to namejust three.

The array may have a characteristic primitive unit cell and a pitch Λ.

The boundary region may comprise, in the transverse cross-section, aplurality of relatively high refractive index boundary veins joinedend-to-end around the boundary between boundary nodes, each boundaryvein being joined between a leading boundary node and a followingboundary node, and each boundary node being joined between two boundaryveins and to a relatively high refractive index region of the photonicbandgap structure. Thus, a vein sits between two nodes, with no othernode between the two nodes; i.e., it sits between two neighboring nodes.

At least one of the boundary veins may comprise, along its length or atits end, a nodule. The nodule may have a substantially elliptical shapein the transverse cross-section, such that an ellipse having a majoraxis of length L and a minor axis of length W substantially fits to theshape of the nodule. The major axis may extend along the boundary veinin which the nodule is situated.

The waveguide may guide light at a wavelength λ₁, which may be anywavelength at which the waveguide is substantially transparent. Thewavelength λ₁, may be in the ultraviolet, visible or infrared parts ofthe electromagnetic spectrum. The wavelength λ₁ may be in a telecomswindow, for example λ₁ may be in the range 1510 nm to 1610 nm or in the1300 nm band. Alternatively, the wavelength λ₁ may be in the 1060 nmband or in the 810 nm band. Operation may be at a longer wavelength, forexample in the range 1.8 to 2.0 μm or in the range 2 μm to 5 μm, at oraround the wavelength of operation of CO₂ lasers (10.6 μm).

The waveguide may be arranged to guide light at a wavelength λ₂, whereinlight guided at the wavelength λ₂ exhibits lower loss than light guidedin the waveguide at any other wavelength.

The lengths of the minor and major axes of an elliptical nodule on aboundary vein have been found to be significant in increasing thefraction of light in the regions of low refractive index and indecreasing the F-factor. In particular it has been found that, in aplane having orthogonal axes along which values of W and L are plotted,particular regions comprise particular pairs of values of W and L(represented by co-ordinates (L,W) in the plane) that provide a higherfraction of light in the regions of low refractive index, or a lowerF-factor, than is found in prior-art waveguides. Table 1 sets outrelations between W and L that conveniently define those particularregions. Various regions of interest may be defined more precisely bytaking combinations of two or more of those relations.

Some of the relations are defined in terms of a parameter X, which isused for brevity, to reduce the number of claims necessary to coverenvisaged possibilities. Thus, parameter X may be equal to thewavelength λ₁ or the wavelength λ₂ or, where the waveguide has a pitch Λas described above, the pitch Λ.

TABLE 1 Relations defining preferred regions of the L-W plane (N.B. Therelations are set out in two columns purely for conciseness; therelations in adjacent columns are as independent of each other as areall other relations in the table). W ≈ L${L \times W} \approx \frac{X^{2}}{12}$ W ≦ 0.467L L × W ≦ 0.113X²$W \approx \frac{L}{3}$$W \leq {( {\frac{1}{18} + \frac{L}{3}} )X}$ W ≧ 0.238L$W \geq {( {{- \frac{1}{18}} + \frac{L}{3}} )X}$$L \geq \frac{5\; X}{12}$$W \geq {( {\frac{5}{18} - \frac{L}{3}} )X}$$L \approx \frac{X}{2}$$W \leq {( {\frac{7}{18} - \frac{L}{3}} )X}$$L \leq \frac{7X}{12}$ W ≧ (−0.133 + 0.467L)X $W > \frac{X}{18}$ W ≦(0.095 + 0.238L)X $W > \frac{5X}{36}$ W ≧ (0.333 − 0.467L)X$W \approx \frac{X}{6}$ W ≦ (0.333 − 0.238L)X $W \leq \frac{7X}{36}$ W≧ (0.467 − 0.467L)X L × W ≧ 0.058X² W ≦ (0.238 − O.238L)X L < 0.27Λ W <0.11Λ L > 0.45Λ W > 0.21Λ

The F-factor of a structure may be improved by increasing the size ofthe core. The core may have, in the transverse cross-section, an areathat is significantly greater than the area of at least some of therelatively low refractive index regions of the photonic bandgapstructure. The core may have, in the transverse cross-section, an areathat is greater than twice the area of at least some of the relativelylow refractive index regions of the photonic bandgap structure.

The core may have, in the transverse cross-section, an area that isgreater than the area of each of the relatively low refractive indexregions of the photonic bandgap structure.

The core may have, in the transverse cross-section, a transversedimension that is greater than the pitch Λ.

The core may correspond to the omission of a plurality of unit cells ofthe photonic band-gap structure, for example, the core may correspond tothe omission of three, four, six, seven, ten, twelve, nineteen or thirtyseven unit cells of the photonic band-gap structure. The core maycorrespond to the omission of more than thirty seven unit cells of thephotonic band-gap structure.

At least some of the relatively low refractive index regions may bevoids filled with air or under vacuum.

At least some of the relatively low refractive index regions may bevoids filled with a liquid or a gas other than air. The region ofrelatively low refractive index that makes up the core may comprise thesame or a different material compared with the regions of relatively lowrefractive index in the photonic bandgap structure.

In some embodiments, at least some of the relatively high refractiveindex regions comprise silica glass. The glass may be un-doped or dopedwith index raising or lowering dopants. As used herein ‘silica’encompasses fused silica, including doped fused silica, and silicateglasses in general such as germano-silicates and boro-silicates.

In alternative embodiments of the invention the relatively highrefractive index regions comprise a material other than silica. Forexample, it may be an inorganic glass in which multi-phonon absorptiononly becomes significant at wavelengths significantly longer than forsilica. Exemplary inorganic glasses may be in the category of halideglasses, such as a fluoride glass, for example ZBLAN. Alternatively, therelatively high refractive index may comprise another solid material,for example an organic polymer.

The relatively low refractive index regions may make up more than 58% byvolume of the photonic bandgap structure. The relatively low refractiveindex regions may make up more than 60%, more than 64%, more than 65%,more than 70%, more than 75%, more than 80%, more than 85%, more than90%, more than 91%, more than 92%, more than 93%, more than 94%, or evenmore than 95%. The relatively low refractive index regions may makearound 87.5% by volume of the photonic bandgap structure.

The waveguide may support a mode having a mode profile that closelyresembles the fundamental mode of a standard optical fiber. An advantageof this is that the mode may readily couple into standard, single modeoptical fiber.

Alternatively, or in addition, the waveguide may support anon-degenerate mode. This mode may resemble a TE₀₁ mode in standardoptical fibers.

Preferably, in either case, said mode supports a maximum amount of themode power in relatively low refractive index regions compared withother modes that are supported by the waveguide.

At least some of the boundary veins may be substantially straight. Insome embodiments, substantially all of the boundary veins aresubstantially straight. Alternatively, or additionally, at least some ofthe boundary veins may be bowed outwardly from, or inwardly towards, thecore defect.

At least two of the higher index regions in the photonic bandgapstructure may be connected to each other.

The higher index regions in the photonic bandgap structure may beinterconnected.

Also according to the invention there is provided an optical fibercomprising a waveguide of a type described above as being according tothe invention.

Also according to the invention there is provided a transmission linefor carrying data between a transmitter and a receiver, the transmissionline including along at least part of its length such a fiber.

Also according to an embodiment of the invention there is provided dataconditioned by having been transmitted through such a waveguide. As inany transmission system, data that is carried by the system acquires acharacteristic ‘signature’ determined by a transfer function of thesystem. By characterizing the system transfer function sufficientlyaccurately, using known techniques, it is possible to match a model ofthe input data, operated on by the transfer function, with real datathat is output (or received) from the transmission system.

Also according to an embodiment of the invention there is provided amethod of forming elongate waveguide, comprising the steps:

forming a preform stack by stacking a plurality of elongate elements;

omitting, or substantially removing at least one elongate element froman inner region of the stack; and

heating and drawing the stack, in one or more steps, into a waveguide ofa type described above as being according to the invention.

Also according to an embodiment of the invention there is provided amethod of forming elongate waveguide for guiding light, comprising thesteps:

(a) simulating the waveguide in a computer model, the waveguidecomprising a core, comprising an elongate region of relatively lowrefractive index and a photonic bandgap structure arranged to provide aphotonic bandgap over a range of wavelengths of light, the structurecomprising elongate regions of relatively low refractive indexinterspersed with elongate regions of relatively high refractive index,including a boundary region of relatively high refractive index thatsurrounds, in a transverse cross-section of the waveguide, the core,wherein properties of the boundary region are represented in thecomputer model by parameters;

(b) finding a set of values of the parameters that, according to themodel, increases or maximises how much of the light guided by thewaveguide is in the regions of relatively low refractive index in thewaveguide.

Also according to the invention, there is provided a method of formingelongate waveguide for guiding light, comprising the steps:

(a) simulating the waveguide in a computer model, the waveguidecomprising a core, comprising an elongate region of relatively lowrefractive index, and a photonic bandgap structure arranged to provide aphotonic bandgap over a range of frequencies of light, the structurecomprising elongate regions of relatively low refractive indexinterspersed with elongate regions of relatively high refractive index,including a boundary region of relatively high refractive index thatsurrounds, in a transverse cross-section of the waveguide, the core,wherein properties of the boundary region are represented in thecomputer model by parameters;

(b) finding a set of values of the parameters that, according to themodel, decreases or minimises the F-factor of the waveguide.

The boundary region may comprise, in the transverse cross-section, aplurality of relatively high refractive index boundary veins joinedend-to-end around the boundary between boundary nodes, each boundaryvein being joined between a leading boundary node and a followingboundary node, and each boundary node being joined between two boundaryveins and to a relatively high refractive index region of the photonicbandgap structure and at least one of the boundary veins comprising,along its length, a nodule, the nodule having a substantially ellipticalshape in the transverse cross-section, such that an ellipse having amajor axis of length L and a minor axis of length W substantially fitsto the shape of the nodule in the transverse cross-section. Theparameters for which values are found may comprise L and W.

Also according to an embodiment of the invention there is provided anelongate waveguide for guiding light comprising:

a core, comprising an elongate region of relatively low refractiveindex; and

an outer structure comprising elongate regions of relatively lowrefractive index interspersed with elongate regions of relatively highrefractive index, including a boundary region comprising a continuousshell of relatively high refractive index that surrounds, in atransverse cross-section of the waveguide, the core;

characterized in that the boundary region comprises a feature or has ashape that is antiresonant at a wavelength of light guided in thewaveguide.

The boundary region is a continuous shell of relatively high refractiveindex in that it does not comprise regions of relatively low refractiveindex: all relatively-high-index regions in the boundary are connectedto each other only by relatively-high-index regions. The core is takento be contiguous with the boundary region. The core thus comprises allconnected regions of relatively low refractive index that are surroundedby the boundary region. The boundary region may be not smooth: it mayfor example be corrugated, with indented regions (for example, formed byomitting every other vein from an innermost polygon of the cladding,such as what would, if all veins were present, be an hexagon defining anhexagonal core), or it may have one two or more struts that projecttowards the center of the core (which struts may be of uniform thicknessor may have nodules at some point along their length, for example attheir ends). Thus, the core need not be of a regular cross section butmay, for example, have projections and indentations defined by theboundary region.

Thus the boundary region may be corrugated with 2, 3, 4, 5, 6, 7, 8, 9,10 or more recesses or indentations, which may be arranged at regularintervals around the center of the core.

The outer structure may exhibit a photonic band-gap. Even if the outerstructure is not a photonic bandgap structure, any features set outabove in relation to other aspects of the invention having a bandgapstructure may be found in the present further aspect of the inventionunless that is not physically meaningful.

The boundary region may have a different structure from the structure ofthe rest of the outer structure. For example, the regions of relativelyhigh refractive index in the boundary region may be thicker or thinnerthan corresponding regions in the rest of the outer structure. Theregions of relatively high refractive index may include nodes or nodulesthat are in different positions or have different sizes fromcorresponding features in the rest of the outer structure (it may bethat there are no corresponding features in the outer structure or thatthere are such features in the outer structure but they are not presentin the boundary region). The regions of relatively high refractive indexin the boundary region may include a region of a different refractiveindex from the refractive index of corresponding region in the outerstructure.

The boundary region may comprise a nodule. The boundary region maycomprise 2, 3, 4, 5, 6, 7, 8, 9, 12 or more nodules, which may bearranged at regular intervals around the center of the core. The nodulesmay be arranged at the centers of veins, where each vein extends betweentwo nodes.

Alternatively, the nodules may be arranged off-center on such a vein.The nodules may be arranged such that the waveguide has in cross-sectionno more than two-fold rotational symmetry. The waveguide may then bebirefringent.

The outer structure may comprise a periodic array of unit cells. Thecore may be of a size larger than one such unit cell, larger than 7 suchunit cells (which corresponds to a central cell and six surroundingcells in a hexagonal arrangement) or even larger than 19 such unit cells(which corresponds to a central cell and two rings of surrounding cellsin a hexagonal arrangement). The waveguide may comprise a jacket aroundthe outer structure.

It may be that the boundary region comprises more or fewer than sixnodules.

Also according to an embodiment of the invention there is provided aphotonic crystal fiber comprising:

an outer structure comprising a periodic array of unit cells, each unitcell comprising a central region of a vacuum or a fluid and an outerregion of a solid material, the periodic array having a pitch Λ; and

a core, comprising an elongate region of a vacuum or a fluid;

the outer structure including a boundary region comprising a pluralityof veins of relatively high refractive index that surrounds, in atransverse cross-section of the waveguide, the core;

characterized in that the veins include nodules that are antiresonant ata wavelength of light guided in the waveguide.

The unit cells may be hexagonal. The central region of the unit cell maybe air. The central region of the unit cell may be circular with adiameter d. The nodules may be elliptical in cross-section. The ellipsemay have a major axis of length 5Λ/12. The ellipse may have a minor axisof length Λ/6. The core may have the same size and shape as a group ofseven unit cells of the outer structure. The waveguide may guide lightin the C-band telecoms window, around 1550 nm (1530 nm to 1570 nm). Thewaveguide may guide light having a wavelength in the range 3 μm to 5 μm.The vacuum or fluid may fill the outer structure to a filling fractionof about 92%. The ratio d/A may be about 0.97. The pitch Λ may be about3 μm. The diameter of the core may be about 9 μm. The unit cell centralregion diameter may be about 2.9. The veins may be of substantiallyconstant thickness over about half their length. If the pitch Λ is 3 μmwhen the waveguide is designed to operate at 1550 nm, then pitches maybe found that are suitable for operation at other wavelengths in similarwaveguide structures by scaling the pitch Λ in proportion to thewavelength, i.e., a corresponding pitch for light of 3 μm would be 6 μm,if the filling fraction of the vacuum or fluid and the ratio d/Λ remainconstant and the refraction index is essentially unaltered.

Any of the features described above are applicable interchangeably toany of the above-described aspects of the invention (except where thatis nonsensical).

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described, by way ofexample only, with reference to the accompanying drawings, of which:

FIG. 1 is a diagram of a transverse cross section of a known PBG fiberstructure;

FIG. 2 is a diagram which illustrates how various physicalcharacteristics of PBG fibers are defined herein;

FIGS. 3, 4 and 5 show diagrams of various examples of PBG fiberstructures;

FIGS. 6 and 7 show mode spectra plots for the PBG fiber structures ofFIGS. 3 and 4;

FIG. 8 shows mode intensity distribution plots for a mode, supported byeach structure of FIGS. 3 and 4, which supports the highest amount oflight in air;

FIGS. 9 and 10 show graphs of mode intensity for x and y axes of thedistributions of FIG. 8;

FIG. 11 shows mode spectra plots for the PBG fiber structures of FIG. 5;

FIGS. 12, 13 and 14 show mode intensity distribution plots for a numberof modes for each of the structures in FIG. 5;

FIG. 15 shows four alternative PBG fiber structures;

FIG. 16 shows four further alternative PBG fiber structures;

FIG. 17 is a diagram of a pre-form suitable for making a known PBGfiber;

FIG. 18 is a diagram of a pre-form suitable for making a fiber accordingto examples of PBG fibers described hereinafter;

FIG. 19 is an alternative pre-form suitable for making a fiber accordingto examples of PBG fibers described hereinafter;

FIG. 20 a is a photograph of a portion of a preform, according to anembodiment of the present invention, taken through a microscope;

FIG. 20 b is a scanning electron micrograph (SEM) image of a portion ofa PBG fiber made using the preform of FIG. 20 a;

FIGS. 21 to 25 are diagrams of alternative pre-forms suitable for makingfibers according to embodiments of the present invention;

FIG. 26 is a diagram of an outer region of a pre-form stack according toembodiments of the present invention, wherein the stack is contained ina large, thick-walled capillary and interstitial regions between theinner surface of the large, thick-walled capillary and the stack containvarious sizes of solid packing rod; and

FIG. 27 shows diagrams of the various beads that were incorporated inthe fiber structures described hereinafter;

FIG. 28 is a graph showing the physical dimensions of the beads shown inFIG. 27;

FIG. 29 is a graph plotting the variation in F-factor for fiberstructures comprising around a core boundary beads according to FIG. 27;

FIG. 30 is a graph plotting the variation in F-factor for fiberstructures comprising around a core boundary other beads according toFIG. 27;

FIG. 31 is a chart which plots the minimum F-factors achieved by fibersincorporating beads shown in FIG. 27;

FIG. 32 is a diagram of a transmission system that can be adapted toincorporate a fiber according to the present invention.

FIG. 33 is a schematic diagram of some examples of corral systemscomprising dielectric cylinders in air (the dashed lines are used forgeometric construction purposes);

FIG. 34 is a plot showing the imaginary part of the effective mode indexneff for a corral system comprising six identical silica cylinders inair arranged hexagonally; the distance between the cylinders is Λ=3.0,4.5 and 6.0 μm and the wavelength is λ=1.55 μm; Im[neff], which isplotted against cylinder diameter d, is related to Im[β] by

${{{Im}\lbrack n_{eff} \rbrack} = \frac{\lambda \; {{Im}\lbrack\beta\rbrack}}{2\; \pi}};$

also shown is Im[β] for a dielectric ring of diameter R=4.5 μm vs. itsthickness d;

FIG. 35 is a plot showing intensity profiles for two corral arrangementsof silica cylinders at anti-resonance; the circles show the positions ofthe cylinder interfaces; the appearance of near nulls close to eachcylinder interface is clear; the wavelength was chosen to be λ=1.55 μm;

FIG. 36 is a plot of the imaginary part of the effective mode index nefffor a corral system comprising 12 identical silica cylinders in airarranged as in the two examples shown in FIG. 35, plotted as a functionof the cylinder diameter d and an operating wavelength of λ=1.55 μm;

FIG. 37 is a diagram that illustrates how an ellipse is fitted tonodules in the structure of FIG. 1;

FIG. 38 is a diagram that illustrates how various physicalcharacteristics of PBG fibers are defined herein;

FIG. 39 is a plot of fraction of light in air for a fiber according toan embodiment of the invention, the plot having axes showing lengths ofthe major axis L and the minor axis W of the ellipse of FIG. 38;

FIG. 40 is a plot of F-factor for a fiber according to an embodiment ofthe invention, the plot having axes showing lengths of the major axis Land the minor axis W of the ellipse of FIG. 38;

FIGS. 41( a) and (b) show various regions of interest in the L-W planeof FIGS. 39 and 40;

FIG. 42 is a diagram of a transverse cross section of a second PBG fiberstructure according to an embodiment of the invention;

FIG. 43 is a plot of (i) field intensity (linear plot), (ii) azimuthallyaveraged field intensity (log. plot) and (iii) distribution of F-factor(linear plot) for ((a) and (b)) two orthogonal polarisation modessupported by the fiber of FIG. 42;

FIG. 44 is a diagram of a transverse cross section of a third PBG fiberstructure according to an embodiment of the invention;

FIG. 45 is a diagram of a transverse cross section of a fourth PBG fiberstructure according to an embodiment of the invention;

FIG. 46 is a diagram of a transverse cross section of a fifth PBG fiberstructure according to an embodiment of the invention;

FIG. 47 is a diagram of a transverse cross section of a sixth PBG fiberstructure according to an embodiment of the invention;

FIG. 48 is a diagram of another pre-form suitable for making a fiberaccording to embodiments of the present invention; and

FIG. 49 a is a microscope photograph of a glass rod attached to theouter periphery of a core boundary in a PBG fiber preform, suitable forforming an antiresonant bead in a PBG fiber structure and FIG. 49 b is ascanning electron microscope image of such a bead in a PBG fiber.

BEST MODE FOR CARRYING OUT THE INVENTION, & INDUSTRIAL APPLICABILITY

FIG. 1 is a representation of a transverse cross-section of a fiberwaveguide structure. In the Figure, the black regions represent fusedsilica glass and the white regions represent air holes in the glass. Asillustrated, the cladding 100 comprises a triangular array of generallyhexagonal cells 105, surrounding a seven-cell core defect 110. A coredefect boundary 145 is at the interface between the cladding and thecore defect. The core defect boundary has twelve sides—alternatingbetween six relatively longer sides 140 and six relatively shorter sides130- and is formed by omitting or removing seven central cells; an innercell and the six cells that surround the inner cell. The cells wouldhave typically been removed or omitted from a pre-form prior to drawingthe pre-form into the fiber. As the skilled person will appreciate,although a cell comprises a void, or a hole, for example filled with airor under vacuum, the voids or holes may alternatively be filled with agas or a liquid or may instead comprise a solid material that has adifferent refractive index than the material that surrounds the hole.Equally, the silica glass may be doped or replaced by a different glassor other suitable material such as a polymer, e.g. an organic polymer.For the sake of simplicity of description herein, however, the followingexemplary embodiments are silica and air fibers.

This region of the cladding, although not shown in its entirety,typically extends outwardly to provide a specified degree of lightconfinement; where more cladding layers provide increased confinement.Typically, although not shown, there are further cladding layerssurrounding the photonic band-gap structure. There may be an additionalsolid silica layer to provide strength and a coating layer to protectthe silica and prevent light entering the fiber from the side, as in anormal fiber.

The waveguide of FIG. 1 has a substantially periodic structurecomprising a triangular lattice of generally hexagonal holes. However,as discussed above, N. M. Litchinitser et al. have demonstrated thatphotonic bandgaps may be achieved in non-periodic structures. Theproperties of the core-cladding boundary are also important innon-periodic PBG structures and the invention is not limited tosubstantially periodic structures but encompasses structures with someor even a high degree of aperiodicity or irregularity in the claddingstructure. However, the exemplary embodiments illustrated hereafter usea triangular lattice of the kind shown in FIG. 1, which will be familiarto the skilled artisan, in order not to obscure the present invention.

Hereafter, and with reference to FIG. 1, a region of glass 115, 175between any two holes is referred to as a “vein” and a region of glass120 where at least three veins meet is referred to as a “node”.

A vein can be generally characterised by its transverse, cross-sectionallength and thickness at a midpoint between the two nodes to which it isattached. Veins tend to increase in thickness from their midpoint to thenodes, although a region of substantially constant thickness at themiddle of the vein tends to appear and then increase in length withincreasing air-filling fraction. Nodes can be generally characterised bya transverse cross-sectional diameter, which is the diameter of thelargest inscribed circle that can fit within the node. In the fiberstructures investigated herein, node diameter is typically larger thanthe thickness of the veins attached to the node.

The core defect boundary 145 comprises the inwardly-facing veins of theinnermost ring of cells that surround the core defect 110.

In practice, for triangular lattice structures that have a largeair-filling fraction, for example above 75%, most of the cladding holes105 assume a generally hexagonal form, as shown in FIG. 1, and the veinsare generally straight.

FIGS. 2 a and 2 b are diagrams which illustrate how various dimensionsof the cladding structure of FIG. 1 are defined herein, with referenceto four exemplary cladding cells 200.

For the present purposes, a node 210′ in the cladding, which is referredto herein as a “cladding node”, is said to have a diameter measurement ddefined by the largest diameter of inscribed circle that can fit withinthe glass that forms the node. A vein 205 in the cladding, which isreferred to herein as a “cladding vein”, has a length l, measured alongits center-line between the circles of the cladding nodes 210 & 210′ towhich the cladding vein is joined and a thickness, t, measured at itsmid-point between the respective cladding nodes. Generally, herein,veins increase in thickness towards the nodes to which they are joined.

The mid-point of a cladding vein is typically the thinnest point alongthe vein. Unless otherwise stated herein, generally, a specified veinthickness is measured at the mid-point of the vein between the two nodesto which the vein is joined.

According to FIG. 2, a cladding node is surrounded by three notionalcircular paths 215, each one being positioned between and abutting adifferent pair of neighboring cladding veins that join the node. Thesethree paths, in effect, define the ‘roundness’ of the corners of thecladding holes and abut the notional inscribed circle that defines thediameter of the respective node. More particularly, the periphery of thenode between each pair of veins is defined by the portions of thecircular paths 215 which begin at a point p and end at a point q alongfirst and second veins respectively. Points p and q are equidistant fromthe center of the node 210′. It will be appreciated that the diameter,d, of the node 210′ is a function of the thickness, t, of the veins, thedistance of p from the center of the node and the pitch Λ, or center tocenter distance between neighboring cells, of the structure.

The cells forming the innermost ring around the boundary of the coredefect, which are referred to herein as “boundary cells”, have one oftwo general shapes. A first kind of boundary cell 125 is generallyhexagonal and has an innermost vein 130 that forms a relatively shorterside of the core defect boundary 145. A second kind of boundary cell 135has a generally pentagonal form and has an innermost vein 140 that formsa relatively longer side of the core defect boundary 145.

Referring again to FIG. 1, there are twelve boundary cells 125, 135 andtwelve nodes 150, which are referred to herein as “boundary nodes”,around the core defect boundary 145. Specifically, as defined herein,there is a boundary node 150 wherever a vein between two neighboringboundary cells meets the core defect boundary 145. In FIG. 1, theseboundary nodes 150 have slightly smaller diameters than the claddingnodes 160. Additionally, there is an enlarged region 165, “bead” or“nodule”, of silica at the mid point of each relatively longer side ofthe core defect boundary 145. These nodules 165 coincide with themid-point along the inner-facing vein 140 of each pentagonal boundarycell 135. The nodules 165 may result from a possible manufacturingprocess used to form the structure in FIG. 1, as will be described inmore detail below. For the present purposes, the veins 130 (170) & 140that make up the core defect boundary are known as “boundary veins”.

In the prior art, photonic band-gap fibers typically comprise eitherplural concentric layers of dielectric material surrounding a core, toform an omni-directional waveguide, or a microstructured photonicband-gap cladding, comprising a triangular lattice of hexagonal holes,surrounding a core region. In the latter kind of band-gap fiber, thereis a core defect boundary but the shape and form of the boundary hastypically been a simple function or artefact of the pre-form andmanufacturing process used to make the fiber.

As will be described below, it is possible to control the diameters ofparticular nodes and the existence or size of beads or nodules along thecore defect boundary during manufacture of a fiber.

The structure in FIG. 1 and each of the following examples of differentstructures closely resemble practical optical fiber structures, whichhave either been made or may be made according to known processes or theprocesses described hereinafter. The structures share the followingcommon characteristics:

a pitch Λ of the cladding chosen between values of approximately 3 μmand 6 μm (this value may be chosen to position core-guided modes at anappropriate wavelength for a particular application);

a thickness t of the cladding veins of 0.0586 times the chosen pitch Λof the cladding structure (or simply 0.0586Λ);

an AFF in the cladding of approximately 87.5%; and

a ratio R having a value of about 0.5.

Referring to FIG. 2, R is defined as the ratio of the distance of p′from the center of the nearest cladding node to half the length of acladding vein, l/2; where p′ is a point along the center-line of acladding vein and is defined by a construction line that passes throughthe center-line of the vein, the center of circle 215 and the point pwhere the circle meets the vein.

In effect, R is a measure of the radius of curvature of the corners ofthe hexagonal cells within the cladding. It will be apparent that themaximum practical value of R is 1, at which value the radius ofcurvature is a maximum and the cladding holes are circular. The minimumvalue of R is dictated by the thickness t and length l of the veins andis the value at which the diameter of the circle 215 tends to zero andthe cladding holes are hexagonal.

For all values of R below the maximum value, the veins appear to have aregion of generally constant thickness about their mid-points, whichincreases in length with decreasing R. For example, a value of R=0.5provides that around half the length of a vein, about its mid-point, hasa substantially constant thickness. Likewise, a value of R=0.25 providesthat around three quarters of the length of a vein, about its mid-point,has a substantially fixed thickness.

Given R, t and Λ, for practical purposes, the diameter d of the claddingnodes is found to be approximately:

$\begin{matrix}{d = {\frac{2\; R\; \Lambda}{\sqrt{3}} - {\Lambda \; R} + t}} & ( {{Equation}\mspace{14mu} 1} )\end{matrix}$

In FIG. 1, the diameter of each boundary node 150, d_(e), is smallerthan the diameter of the cladding nodes 160, due to there being lessglass available at the boundary for forming the nodes. A model similarto that shown in FIG. 2 may if required be used to define the form ofthe boundary nodes. The differences between FIG. 2 and the model for theboundary nodes are (1) the boundary node model includes the core defect110 and two boundary cells rather than three cladding cells, (2) it isassumed that the value of R is a minimum, such that there is nomeasurable circular path inside the core defect 110; and, (3) theinternal angles of the core defect and the boundary cells are differentfrom each other and from the cells in the cladding.

The beads 165 shown in FIG. 1 are substantially oval shaped, each havinga major dimension which is approximately ⅓ the length of the distancebetween the two node centers that lie on either side of the bead and aminor dimension which is ⅓ the length of the major dimension. The minordimension of the bead, which defines the thickness of the associatedvein at its mid-point, is slightly longer than the diameter of therespective boundary nodes 150.

For boundary veins with no beads, the thickness at the mid-point of thevein between boundary nodes is the same as the thickness of the claddingveins at the same point.

The present inventors have determined that it is possible to control theperformance of PBG fibers in particular by aiming to maximise the amountof light that propagates in air within the fiber structure, even if somelight is not in the core, in order to benefit from the properties of PBGfibers, such as reduced absorption, non-linearity and, in addition,reduced mode coupling.

For the purposes of comparing aspects of the performance of variousdifferent structures it is useful to consider the modes that aresupported in the band gap of various PBG fiber structures. This may beachieved by solving Maxwell's vector wave equation for the fiberstructures, using known techniques. In brief, Maxwell's equations arerecast in wave equation form and solved in a plane wave basis set usinga variational scheme. An outline of the method may be found in Chapter 2of the book “Photonic Crystals—Molding the Flow of Light”, J. D.Joannopoulos et al., ©1995 Princeton University Press.

FIGS. 3 and 4 illustrate six exemplary PBG fiber structures that will beconsidered hereafter. FIG. 3 illustrates three structures identified asS1, S2 and S3 herein, which are seven-cell core defect structures. S1 isthe same as the structure illustrated in FIG. 1 and is reproduced inFIG. 3 for convenience only. S2 and S3 reinforce various characteristicsof the invention, as determined by the present inventors, and, inparticular, are discussed herein in order to illustrate how the modespectrum of a given structure may vary significantly without varying thesize of the core defect but, instead, varying different core defectboundary characteristics.

FIG. 4 illustrates three structures identified as S4, S5 and S6, eachhaving a nineteen-cell core defect. S4 is an exemplary embodiment of thepresent invention. S4, S5 and S6, apart from core defect size, have thesame cladding characteristics as S1, S2 and S3 respectively. S1 to S3have a maximum core defect radius of about 1.5Λ. In contrast, S4 to S6have a maximum core defect radius of about 2.5Λ.

The characteristics of structures S2 to S6 will now be described infurther detail.

There are a number of differences between the form of the core defectboundary in S1 and the boundary in S2. S2 has reduced boundary nodediameters, which are significantly smaller than the cladding nodes 360,compared with S1, and no apparent beads along the core defect boundary345. According to the definitions provided herein, the boundary nodes355 in S2 have a minimum diameter; the associated values of R are at aminimum and, accordingly, there are no measurable circular pathsdefining the periphery of the nodes. The diameters of the boundary nodes355 in S2 are only very slightly larger than the thickness of theboundary veins 330, 340. In contrast, as for S1, the cladding nodes 360have diameters that are significantly larger than the thickness of theiradjoining veins 315.

It may in practice be difficult to make the exact structure of S2 due tosurface tension effects acting on the glass during the drawing process,which may cause the cladding veins to meet the boundary veins atslightly rounded corners; meaning R is not its theoretical minimum.However, it is useful to compare the characteristics of S2 with theother structures herein. Structures closely resembling S2, however, canbe made according to a method that will be described in detail below.

The boundary in S3 has no apparent beads, as in S2, and the boundarynodes 355 have a similar diameter to those in S1.

The structure in S4 has an additional ring of cladding cells removedfrom around the core defect compared with S1. This forms a core defect410 equivalent to nineteen missing cladding cells. Similar to S1, S4 hasboundary nodes 450 that are significantly larger in diameter than thethickness of the respective boundary veins and there are hexagonal cells425 at each corner of the core defect 410. However, in contrast to S1,which has one generally pentagonal cell along each side of the coredefect boundary 145, S4 has two generally pentagonal cells 435 alongeach side of the core defect boundary 445. In addition, there are twobeads 455 along each side of the core defect boundary 445, roughlycoincident with the mid-point of the vein 440 of each pentagonal cell425 that borders the core defect boundary 445. The minor dimension ofeach bead is slightly longer than the diameter of the nodes to whicheach respective vein is joined. There are also three boundary nodes 455per relatively longer side of the core defect boundary 445, comparedwith two for the seven-cell core defect structures. Overall, S4 haseighteen cells sharing veins with the core defect boundary 445. S4represents an exemplary embodiment of the present invention.

The boundary in S5 is similar to S2 in the respect that it hasreduced-diameter boundary nodes 455′, which do not have diameters thatare significantly larger than the thickness of the respective veins, andthere are no apparent beads. All other parameters of S5 are the same asS4. S5 represents an exemplary embodiment of the present invention.

The boundary in S6 has no apparent beads, as in S3, and the boundarynodes 455 have a similar diameter to those in S1. All other parametersof S6 are the same as S4. S6 represents an exemplary embodiment of thepresent invention.

FIG. 5 illustrates three further nineteen-cell core defect structures,S7, S8 and S9, which have cladding arrangements very similar to those ofstructures S4-S6. The latter two structures are embodiments of thepresent invention. Structure S7 has no beads around the core defectboundary, S8 has enlarged beads around the core defect boundary(compared with the beads in S4) and S9 has two smaller beads in place ofthe single beads per vein of S8. Structures S8 and S9 are embodiments ofthe present invention.

FIGS. 6 and 7 each show three mode spectra, identified as P1 to P3 andP4 to P6 respectively. Each spectrum P1 to P6 relates to a respectivePBG fiber structure S1 to S6. The horizontal axis of each spectrum isnormalised frequency, ωΛ/c, where w is the frequency of the light, Λ isthe pitch of the cladding structure, and c is the speed of light in avacuum. The vertical axis of each spectrum relates to the response ofthe structure to a given input for a given normalised wave-vector βΛ=13,against which the spectrum is plotted, where β is the chosen propagationconstant for the calculations. The spectra are produced using aFinite-difference Time Domain (FDTD) algorithm, which computes thetime-dependent response of a given hollow core structure to a giveninput. This technique has been extensively used in the field ofcomputational electrodynamics, and is described in detail in the book“Computational Electrodynamics: The Finite-Difference Time-DomainMethod”, A. Taflove & S. C. Hagness, ©2000 Artech House. The FDTDtechnique may be readily applied to the field of PBG fibers andwaveguides by those skilled in the art of optical fiber modelling.

With reference to spectra P1 to P6, each vertical spike indicates thepresence of at least one mode at a corresponding normalised frequency.In some cases, multiple modes may appear as a single spike or as arelatively thicker spike compared with other spikes in a spectrum. Thisis due to the fact that the data used to generate the spectra is not ofa high enough resolution to distinguish very closely spaced modes. Assuch, the mode spectra should be taken to provide only an approximationto the actual numbers of modes that exist for each structure, which issatisfactory for enabling a general comparison between spectra herein.

On each spectrum, a ‘light line’ for the respective structure is shownas a solid vertical line at ωΛ/c=13=βΛ, and band edges, which bound abandgap, are represented as two dotted vertical lines, one on eitherside of the light line, with a lower band edge of the bandgap at aroundωΛ/c=12.92 and an upper band edge of the bandgap at around ωΛ/c=13.30. Abandgap in P1 to P6 is a range of frequencies of light for a given β.For the present examples, the bandgap is slightly wider than 0.35 (inunits of ωΛ/c). The inventors estimate that the minimum practical widthfor a PBG fiber bandgap would be around 0.05 in the present units ofmeasure but, more preferably, would be greater than 0.1.

Modes that are between the light line and the lower band edge (that is,to the left of the light line) will concentrate in the glass and beevanescent in air whereas the modes that are between the light line andthe upper band edge (that is, to the right of the light line) may beair-guiding.

As shown in P1, relating to S1, there are around three modes between thelight line and the lower band edge and around nine modes between thelight line and the upper band edge (taking the thicker spikes as twomodes). It is clear that S1 supports a significant number of modes, someof which could be air-guiding; although, it is unlikely that all ofthese modes will be excited by a given light input. Analysis of theindividual modes shown in the bandgap of P1 leads to a finding that themode marked as F1 is an air-guiding mode, which most closely resemblesthe form of a fundamental mode in a typical standard optical fiber andsupports the maximum amount of light in air. The mode is found to bedegenerate, being one of a pair of very similar modes falling at aboutthe same position in the bandgap.

As shown in P2, relating to S2, approximately two modes lie between thelight line and the lower band edge and there are around twelve modesbetween the light line and the upper band edge. As with S1, S2 supportsa significant number of modes, some of which could be air-guiding. Themode marked F2 in P2 is found to be a degenerate, air-guiding mode thatmost closely resembles the form of a fundamental mode in a typicalstandard optical fiber and supports the maximum amount of light in air.

The structural characteristics of S2 are not that different from thoseof S1; the only differences being the reduced boundary node sizes in S2and omission of the beads. Notably, the core defect diameters of the twostructures are the same. However, the mode spectra for the twostructures are significantly different, there being morepotentially-air-guiding modes supported by S2 but fewer modes that areevanescent in air.

As shown in P3, relating to S3, there are around three modes between thelight line and the lower band edge and around thirteen modes between thelight line and the upper band edge. Again, it is clear that S3 supportsa significant number of modes, some of which could be air-guiding. Themode marked F3 in P3 is a degenerate, air-guiding mode that most closelyresembles the form of a fundamental mode in a typical standard opticalfiber and supports the maximum amount of light in air.

Again, the structural characteristics of S3 are only subtly differentfrom those of either S1 or S2, with the core defect diameters of allstructures being the same. However, the mode spectrum for S3 is, oncemore, significantly different from the mode spectra of either S1 or S2.

As shown in P4, relating to S4, which is a nineteen-cell core defectstructure, there are approximately two to four modes between the lightline and the lower band edge and in excess of twenty modes between thelight line and the upper band edge of the bandgap region. Clearly, S4appears to support significantly more modes than any of the foregoingseven-cell core defect structures. The mode marked F4 in P4 is again adegenerate, air-guiding mode that most closely resembles the form of afundamental mode in a typical standard optical fiber and supports themaximum amount of light in air.

The core defect diameter of S4 is significantly larger than in S1,whereas the other parameters are substantially the same. On the basis ofprior art thinking it is not a surprise that there appear to besignificantly more modes supported in the nineteen-cell core defectstructure of S4 than in any of the seven-cell core defect structures S1to S3.

As shown in P5, relating to S5, there are approximately four modesbetween the light line and the lower band edge and around fifteen totwenty modes between the light line and the upper band edge. Again, S5appears to support significantly more modes than the foregoingseven-cell core defect structures. The mode marked F5 in P5 is adegenerate, air-guiding mode that most closely resembles the form of afundamental mode in a typical standard optical fiber and supports themaximum amount of light in air.

The mode spectra for S4 and S5 are similar in terms of numbers of modes,with both structures supporting a number of evanescent and possiblyair-guiding modes.

As shown in P6, relating to S6, there is a single mode between the lightline and the lower band edge and approximately twelve to fifteen modesbetween the light line and the upper band edge. Thus, S6 appears tosupport significantly fewer modes than either of S4 or S5, even thoughthe core defect sizes are the same. Surprisingly, the mode spectrum ofS6 appears to resemble, in both numbers and positions of modes, the modespectrum of S2, which is a seven-cell core defect structure. This iscontrary to prior art thinking, which indicates that larger core defectsshould support, proportionately, more modes. The mode marked F6 in P6 isagain a degenerate, air-guiding mode that most closely resembles theform of a fundamental mode in a typical standard optical fiber andsupports the maximum amount of light in air.

On the basis of the above six examples of different PBG fiberstructures, it is clear that the numbers and locations of modes in amode spectrum are not determined only by size of the core defect, indexdifference between a core and cladding and wavelength of light; evenwhen the cladding structure is fixed. Taking S1 to S3, for example, itis clear that the locations of modes and, in particular, the number ofmodes that are likely to be evanescent in air or possibly air-guiding,can be varied significantly by varying the node size, and presence orabsence of beads, about the core defect boundary, without the need tovary the core defect size. Additionally, while certain PBG fiberstructures that support a greater number of modes—especially potentiallyair-guiding modes—may be made by increasing the core defect size for anygiven cladding structure, it also appears possible to increase the coredefect size without significantly increasing the number of modes thatare supported by the structure. This is surprising and contrary to thethinking in the prior art.

FIG. 8 comprises six plots, D1 to D6, which show the mode intensitydistributions, over a transverse cross-section of a respective PBG fiberstructure, for modes F1 to F6 respectively. The shading of the plots isinverted, such that darker areas represent more intense light thanlighter regions. Each plot shows the position and orientation of x and yplanes, which correspond to the x and y planes of the structures, asillustrated in FIGS. 3 and 4. These plots were produced using theresults obtained by solving Maxwell's equations for each structure, asdescribed above.

The graphs in FIGS. 9 and 10 show the mode intensity for modes F1 to F6along longitudinal planes x and y of D1 to D6 respectively. Theintensity values are normalised so that the maximum intensity of themode is at 0 dB on the graph; the y-axis scale being logarithmic. Theshaded vertical lines and bands across the graphs coincide with andrepresent the glass regions of the actual respective structure along thex and y planes. For the x and y planes, therefore, it is possible to seehow the light intensity of the mode varies in the air and glass, andacross the glass/air boundaries, of each structure.

Table 2 below shows, for modes F1 to F6, the approximate normalisedfrequency at which the mode lies within the bandgap of its respectivestructure and the percentage of light that is in air rather than in thehigh index silica regions.

TABLE 2 Normalised frequency Mode Number (ω

c) % light in air F1 13.14 92.8 F2 13.12 97 F3 13.11 97.5 F4 13.05 97.7F5 13.04 99.6 F6 13.04 99.5

The percentage of light in air for modes is found by calculating theintegral of the light intensity across only the air regions of the plotsin FIG. 8 and normalising to the total power. Of course, the plots inFIG. 8 represent the intensity across only an inner region of thevarious PBG fiber structures. Accordingly, the respective percentages oflight in air are calculated for the inner regions only and may beslightly different if calculated across entire PBG fiber structuresinstead. However, as will be seen, the intensities have typicallyreduced so considerably towards the edges of the plots that any light inregions outside of the inner regions, whether in air, glass or both, isunlikely to have any significant impact on the percentage of light inair values.

Plot D1 shows the mode intensity distribution for the F1 mode, which wasfound at a normalised frequency ωΛ/c of about 13.14. Plot D1 togetherwith graphs x1 and y1 show that the F1 mode has a generally circularcentral region in the core defect. The central region of the mode isintense at its center and decays sharply towards the core defectboundary. There are two intense satellites to the left and right of thecentral region, coincident with the core defect boundary, and a numberof less intense satellites that form a broken ring around the centralregion. As shown in graph x1, the satellites to the left and right ofthe central region have slightly higher intensities than the maximumintensity of the central region. It is significant to note that theseintense satellites, along with the larger ones of the less intensesatellites around the boundary, appear to coincide with the beads of S1.In addition, it would appear that the remainder of the less intensesatellites appear to coincide with the boundary nodes of S1. There isevidence in D1 of some light being concentrated further out from thecenter of the structure than the core defect boundary although, as issupported by graphs x1 and y1, the light intensity drops-off rapidlyaway from the central region. The light that is outside the core defectappears to coincide with cladding nodes.

It is apparent that, for the seven-cell core defect structure S1, asignificant amount of light concentrates in the pronounced beads. It isapparent, however, that the F1 mode is air-guiding, with a significantfraction of the light existing in the core defect and with a localintensity minimum of the mode falling within the core defect boundary.The intensity of the light in the glass of the cladding structuredecreases significantly moving further away from the core defectboundary.

Plot D2 shows the mode intensity distribution of the F2 mode in thetransverse plane of S2. The mode was found at a normalised frequencyωΛ/c of about 13.12. Plot D2 together with graphs x2 and y2 show thatthe F2 mode has a generally circular central region in the core defect.The central region is intense at its center and decays sharply towardsthe core defect boundary. There are six relatively lower intensitysatellites about the central region, coincident with the core defectboundary, and lower intensity satellites in glass further out from thecentral region. The six satellites around the core defect boundary havea lower intensity than the maximum intensity of the central region, incontrast to the intense satellites of plot D1. It is believed that inplot D2 the intensities of the satellites around the core defectboundary are less than in plot D1 due to the removal of the pronouncedbeads; in-keeping with the observation that, for a seven-cell coredefect structure, a significant amount of light concentrates in thepronounced beads.

As with the F1 mode, it is apparent that the F2 mode is air-guiding. Itis also apparent that some of the light concentrates in the glass of thecladding structure.

The percentage of light in air for the F2 mode is 97%. This value issignificantly larger than the value of 92.8% for the F1 mode even thoughthe core defect size is the same. This increase in the amount of lightin air is attributed to the reduction in diameter of the boundary nodesand omission of the beads. Accordingly, it is expected that S2 will haveimproved loss, non-linearity and mode coupling characteristics comparedwith S1.

Plot D3 shows the mode intensity distribution of the F3 mode in thetransverse plane of S3. The mode was found at a normalised frequencyωΛ/c of about 13.11. The qualitative and quantitative characteristics ofthe F3 mode, as shown in plot D3 and graphs x3 and y3, very closelymatch those of the F2 mode. Similarly, the value of the percentage oflight in air for the F3 mode is 97.5%, which is very close to the figurefor the F2 mode. Accordingly, it is expected that S3 will also haveimproved loss, non-linearity and mode coupling characteristics comparedwith S1.

Plot D4 shows the mode intensity distribution of the F4 mode in thetransverse plane of S4. The mode was found at a normalised frequencyωΛ/c of about 13.05. Plot D4 together with graphs x4 and y4 show thatthe F4 mode has a generally circular central region in the core defect.The central region is intense at its center and decays rapidly towardsthe core defect boundary, although not as rapidly as in Plots D1 to D3.The central region has a local minimum that falls close to and withinthe core defect boundary, which means that the central region of themode in plot D4 has a diameter in the order of two pitches longer thanfor any of the seven-cell core defect structures.

There are a number of low intensity satellites around the central regionin plot D4, which appear to coincide with the boundary nodes of S4. Fromgraphs x4 and y4, these satellites appear to be more than 20 dB lowerthan the peak intensity of the central region. However, it should benoted that the x4 plane does not cross the core defect boundary at abead, whereas planes x1 to x3 do, which means it is not possible to makea direct comparison of satellite intensity between graph x4 and graphsx1 to x3. The fact that the satellites in plot D4 appear so faint,though, does indicate that they have a significantly reduced intensitycompared with satellites in plots D1 to D3.

The F4 mode is apparently air-guiding, with a significant fraction ofthe light existing in the core defect. Light which is guided outside ofthe core defect is concentrated in the glass. The percentage of light inair for S4 is 97.7%. This value is an improvement over the highestseven-cell core defect structure value by a small margin (0.2%) and asignificant improvement (4.9%) over S1, which has a similar boundarynode configuration. Accordingly, it is expected that S4 will haveimproved loss, non-linearity and mode coupling characteristics comparedwith S1.

Plot D5 shows the mode intensity distribution of the F5 mode in thetransverse plane of S5. The mode was found at a normalised frequencyωΛ/c of about 13.04. Plot D5 together with graphs x5 and y5 show thatthe F5 mode is very similar in form to the F4 mode, with an intensecentral region and only very faint satellites outside of the centralregion. These satellites appear fainter than those in plot D4. Like theF4 mode, it is apparent that the F5 mode is air-guiding with asignificant fraction of the light existing in the core defect.

The percentage of light in air for the F5 mode is 99.6%, which issignificantly higher than the value of 97.7% for the F4 mode, eventhough the core defect sizes are the same. This increase in light in airvalue is attributed to the reduction in size of the boundary nodes andomission of the beads in S5 when compared with S4. It is expected thatS5 will have significantly improved loss, non-linearity and modecoupling characteristics compared with S1 and S4.

Plot D6 shows the mode intensity distribution of the F6 mode in thetransverse plane of S6. The mode was found at a normalised frequencyΩΛ/c of about 13.04. Plot D6 together with graphs x6 and y6, relating tothe F6 mode, very closely match the qualitative and quantitativecharacteristics of the F5 mode. In addition, the percentage of light inair for the F6 mode is 99.5%, which is similar to the value for the F5mode. Accordingly, like S5, it is expected that S6 will havesignificantly improved loss, non-linearity and mode couplingcharacteristics compared with S1 and S4, while at the same time notsupporting a significantly increased number of modes compared with theseven-cell core defect structures of Structures S1 to S3.

Table 3 below provides data for six further exemplary waveguidestructures, S10 to S15. The waveguide structures for S10-S15 veryclosely resemble S3, in that the boundaries have no apparent beads andthe boundary nodes have a similar diameter to those in S1. Due to thesimilarity, and for reasons of brevity herein, S10-S15 are notindependently represented in the Figures. The difference between thestructures is only in boundary vein thickness, as shown in Table 3. Thevariations in boundary vein thickness are compensated for by slightvariations in core defect diameter.

In Table 3, boundary vein width is normalised relative to the pitch Λ ofthe structures, which was the same for each structure. Structure S10 hasa boundary vein thickness the same as the cladding vein thickness and,hence, was closest in form to S3. For each structure, the position ofthe mode having the highest percentage of light in air is presented as afrequency that is normalised with respect to the pitch of the structure.

TABLE 3 Boundary Normalised frequency % light Structure Vein Width/

(ω

c) in air S10 0.0383 13.11 98.6 S11 0.0438 13.11 (13.29) 98.2 (97.7) S120.0493 13.10 96 S13 0.0548 13.12 (13.28) 96.9 (98.3) S14 0.0602 13.1197.3 S15 0.0657 13.11 97.8

Discounting for the moment the values in parentheses in Table 3, themodes having the highest percentage of light in air for each structurewere found to be ones which most closely resemble the fundamental modein a standard optical fiber communications system. As can be seen,varying the width of the boundary veins has little effect on theposition of the respective modes. In contrast, however, variation inboundary vein thickness has a significant impact on the percentage oflight in air for the modes. Within the coarse range of boundary veinthicknesses examined, it can be seen that a candidate as a preferredstructure in terms of maximum light in air is S10, which has a boundaryvein thickness of around 0.0383Λ (around 70% of the cladding veinthickness). However, a significant improvement over S13 is also seen ata boundary vein thickness of around 0.0438Λ (around 80% of cladding veinthickness). It is worthy of note, also, that the improvement is notlinear, with the boundary vein thickness of S12 (around 90% of claddingvein thickness) producing a lower percentage of light in air than eitherof S13 or S11. In addition, slight improvements over S13 are seen withS14 and S15, which have thicker boundary veins than S13.

Although not described herein in detail, the inventors have found thatthe mode spectra for structures S10 to S15 vary considerably withvarying boundary vein thickness. The variations were at least as markedas those found by varying the boundary node size and bead presence instructures S1 to S3, which are very similar seven-cell core defectstructures.

Turning now to the values in parentheses in Table 3, for structure S13,a mode having the values shown was found to be non-degenerate and toexist within the bandgap of S13 to the right of the light line. Thismode was found to support the highest fraction of light in air for thestructure.

All other modes, which have been shown herein to support the maximumfraction of light in air, have been degenerate.

As will be appreciated, a non-degenerate mode may find beneficialapplication, for example, in a system that is required to have minimalpolarisation mode dispersion. This is because, once light has beenlaunched or coupled into the non-degenerate mode, there is no scope forpower to couple between degenerate mode pairs, which is the cause ofsuch dispersion in practical systems.

The mode represented by the values in parentheses for S11 was also foundto be non-degenerate. However, for this structure, the value ofpercentage of light in air for this mode was less than the value for themode that most closely resembles the form of a fundamental mode.

It is expected that there are likely to be a number of non-degeneratemodes supported by the present waveguide structures, as will bedescribed hereinafter. However, whether or not the modes exist withinthe bandgap of a particular structure would depend on the relationshipbetween the bandgap and the respective mode spectrum, which, as has beenshown, can be extremely sensitive to core size and boundary form atleast. The non-degenerate modes typically exist at higher frequenciesthan the fundamental-like modes. Similarly, the present inventors havefound that nineteen cell core defect structures also support thesenon-degenerate modes.

Mode spectra P7-P9 for respective structures S7 to S9 are shown in FIG.11. In these spectra, the modes numbered 1 and 2 are degenerate,fundamental-like modes supported by the structure and the other numberedmodes are the modes that are nearest to the fundamental modes. Each ofthe numbered modes has a respective mode intensity plot, identified asDn-m in FIGS. 12 to 14 (where n is the structure number and m is themode number).

Spectra P7, relating to S7, has a degenerate pair of fundamental modesD7-1 and D7-2 just to the right of the light line. To the right of thefundamental modes is a single mode D7-5, which can be identified as aso-called ‘surface mode’, which has a significant portion of its powerin or near to the core defect boundary. Further to the right is a groupof three core guided modes, D7-6 to D7-8. Further to the right isanother surface mode D7-9. To the left of the light line, but stillwithin the bandgap, are two surface modes D7-3 and D7-4. As can be seen,the fundamental modes in this spectrum P7 are reasonably well spacedfrom the other modes that are supported within the bandgap.

Spectrum P8, relating to S8, has the same degenerate pair of fundamentalmodes D8-1 and D8-2 just to the right of the light line. In this case,however, there is a group of four modes: two non-degenerate modes D8-5and D8-8, resembling the TM₀₁ and TE₀₁ modes of a standard opticalfiber, and a degenerate pair of similar looking modes D8-6 and D8-7,which resemble the HE₂₁ modes of a standard optical fiber. This group isfurther away from the fundamental modes that in P7. Just to the left ofthe fundamental modes, but still to the right of the light line, arethree surface modes; D8-3, D8-4 and D8-9.

Spectrum P9, relating to S9, shows the two fundamental modes D9-1 andD9-2, closely surrounded on both sides by surface modes D9-3-D9-6.

From the mode spectra results for structures S7-S9 it is clear that itis possible to vary quite dramatically the modal characteristics of agiven structure by adjusting only the core boundary characteristicsthereof. In particular, while structure S8 has a relatively good spacingof modes from the fundamental pair structure, S9 has a number of surfacemodes in very close proximity to the respective fundamental pair. Thepresent inventors expect, therefore, that structure S9 will experiencefar more loss due to mode coupling of power from the core modes to theboundary modes than either of S7 or S8 at the given operatingwavelength.

The present inventors believe that slight variations on the coreboundary have profound effects on the surface modes because these modesreside primarily in the glass of the core boundary. In contrast, slightvariations in the core boundary are less likely to have an effect of thecore modes, since very little of the light of these modes is in the coreboundary.

In practical optical fiber transmission systems, it is expected that onefixed parameter will be operating wavelength. It is well-known that aPBG fiber can be designed for operation at a given wavelength, forexample at around 1550 nm, since the dimensions of PBG structures simplyscale with wavelength. However, the present inventors anticipate thatthere may be a need to tune a given PBG fiber structure, to optimise itsperformance at the given wavelength; for example, by manipulating thespectral positions of surface modes to move them away from the coremodes of interest. Embodiments of the present invention findparticularly beneficial application as a way of so tuning PBG fibers,independently or in addition to varying core diameter and otherparameters of the fibers.

The structures illustrated in the diagram in FIG. 15 are seven cell coredefect structures according to embodiments of the present invention.

FIG. 15 a has a core boundary which includes six inwardly-facing nodulesalong the six relatively longer boundary veins. FIG. 15 b is a diagramof an alternative structure, having outwardly-facing nodules along sixrelatively shorter boundary veins. FIG. 15 c illustrates a similarstructure, this time having alternating inwardly and outwardly facingnodules along the six relatively shorter boundary veins. FIG. 15 d hasrelatively thick boundary veins extending between pairs of neighboringboundary nodes that coincide with hexagonal boundary cells. In thisembodiment, the thickness of the thicker veins is about 2.5 times thethickness of the other boundary and cladding veins.

The structures illustrated in FIG. 16 are yet further embodiments of thepresent invention. FIG. 16 a-16 c are nineteen cell core defectstructures. FIG. 16 a has a core boundary comprising eighteen boundaryveins and every vein includes a bead. In contrast, FIG. 16 b has whatmight be considered a corrugated core defect boundary, since eachboundary vein comprises a row of closely packed beads: six beads alongeach longer boundary vein and three beads along each shorter boundaryvein. The structure in FIG. 16 c is similar to the structure in FIG. 16b. However, in FIG. 16 c, the beads only project outwardly from the coredefect boundary. It would of course also be possible to provide asimilar structure in which the beads projected only inwardly from thecore defect boundary. FIG. 16 d is an additional seven cell core defectstructure, which has enlarged beads extending between respective pairsof more widely spaced neighboring nodes.

With reference to FIG. 17, prior art structures of the kind exemplifiedby S1 may be made from a pre-form 1700 comprising a stack of hexagonalcapillaries 1705. The hexagonal capillaries 1705 each have a circularbore. The cladding nodes 160 and boundary nodes 150 (from FIG. 1) of thePBG fiber structure result from the significant volume of glass that ispresent in the perform 1700 wherever the corners 1710, 1715 ofneighboring capillaries meet. The beads 165 are formed from the glass ofthe inwardly-facing corners 1720 of the capillaries that bound an innerregion 1725 of the pre-form 1700, which is to become the core defectregion 110 (cf. FIG. 1) of a PBG fiber structure. These corners 1720,and the two sides of each capillary that meet at the corners, recede dueto surface tension as the stack of capillaries is heated and drawn. Suchrecession turns the two sides and the corner 1720 into a boundary vein140, with a bead 165. The inner region 1725 may be formed by omittingthe inner seven capillaries from the pre-form and, for example,supporting the outer capillaries using truncated capillaries at eitherend of the stack, as described in PCT/GB00/01249 (described above) or byetching away glass from inner capillaries in accordance with eitherPCT/GB00/01249 or U.S. Pat. No. 6,444,133 mentioned above. In some priorart structures, the known beads may result from an etching processrather than being entirely due to use of hexagonal capillaries.

While it is possible to adapt the prior art processes in order to makethe nineteen-cell core defect S4, which has beads on some of theboundary veins, the present inventors have appreciated that it would bemore difficult to manufacture any of S5 or S9 using the prior arttechniques. In particular, it would be difficult to control thediameters of boundary nodes using hexagonal cross section capillaries ofthe kind described with reference to FIG. 17. On the other hand, it isdifficult to make structures having cladding nodes with diameters whichare significantly larger than their respective veins by using purelycircular capillaries, especially when the required AFF is high, forexample higher than 75%. In addition, formation of beads or nodules (orthe like) at selected locations around the core boundary is difficultusing prior art processes.

The diagram in FIG. 18 illustrates one way of forming a pre-form stack1800, including a nineteen cell core region 1810, which is suitable forforming a PBG fiber structure S4 or S8. The core region 1810 is formedby assembling circular cross section capillaries 1805 in a close-packedtriangular arrangement around a large diameter core capillary 1815,which is large enough to support capillaries around a region left byremoval of nineteen capillaries: an inner capillary, the six capillariesaround the inner capillary and the twelve capillaries around the sixcapillaries. The cladding capillaries 1805 have an outer diameter ofabout 1 mm and a wall thickness of about 0.05 mm and the large diametercore capillary 1815 has an outer diameter of about 4.5 mm and a wallthickness of about 0.05 mm. The large diameter core capillary 1815supports the cladding capillaries while the stack is being formed andeventually becomes part of the material that forms a core defectboundary.

Interstitial voids 1820 that form at the at the mid-point of eachclose-packed, triangular group of three cladding capillaries are eachpacked with a glass rod 1840, which has an outer diameter of about 0.15mm. The rods 1825 that are packed in voids assist in forming claddingnodes, which have a diameter d that is typically significantly greaterthan the thickness t of the veins that meet at the nodes mission of arod from a void in the cladding leads to the formation of a claddingnode that has a relatively smaller diameter, for example closer to thethickness of the respective adjoining veins.

The rods 1825 may be inserted into the voids after the capillaries havebeen stacked. Alternatively, the stack may be assembled layer by layer,with the rods that rest on top of capillaries being supported by anappropriate jig, for example positioned at either end of the stack,until the next upper layer of capillaries is in place to support thoserods. In commercial scale operations, it is apparent that the manualtask of forming a pre-form stack could readily be automated, usingappropriately programmed robots, for example of the kind used incomponent laying for printed circuit boards.

The interstitial voids 1830 that are formed between the claddingcapillaries 1805 and the large diameter capillary 1815 are not packedwith any rods, thereby minimising the volume of glass that is available,during drawing of the stack 1800, for formation of boundary nodes.

As shown in FIG. 18, the large diameter capillary 1815 has attached toits inner surface twelve silica rods 1835. The rods 1835 are fused tothe inside of the large diameter capillary 1815 in an additional heatingstep before the capillary is introduced to the stack 1800. When thestack 1800 is heated and drawn into fiber, these rods fuse with thelarge diameter capillary 1815, which itself fuses to the inwardly facingsurfaces of the innermost cladding capillaries, to form core boundarybeads of the kind described herein with reference to structures S4 andS8. The rods 1835 can be selectively positioned on the inside of thelarge diameter capillary 1815 to be aligned with either or both of thelonger or shorter core boundary veins. Of course, within practicallimits, any number of rods 1835 may be attached to the inside, or indeedoutside, of the large diameter capillary 1815. If attached on theoutside of the large diameter capillary 1815, the rods 1835 may bealigned with the larger interstitial voids 1830.

The diameters of the rods are selected to provide the required bead sizeand may be of similar size or vary in size around the periphery of thelarge diameter capillary 1815.

In principle, rods 1835 may be attached to the inside or to the outsideof the large diameter capillary 1815. Indeed, rods 1950 (see FIG. 19)may in principle be attached to both the inside and the outside of thesame region of the large diameter capillary, so that they form arelatively larger bead on the core boundary.

FIG. 19 illustrates a similar pre-form stack suitable for forming a PBGfiber according to structure shown in FIG. 15 a.

The pre-form stack 1800 (or 1900) is arranged as described withreference to FIG. 18 (or FIG. 19) and is then over-clad with a further,relatively thick-walled capillary (see, for example, FIG. 26), which islarge enough to contain the stack and small enough to hold thecapillaries and rods firmly in place. The entire over-clad stack is thenheated and drawn into a so-called cane, during which time all therelatively large interstitial voids 1830 and any remaining voids betweenthe glass rods 1825 and the cladding capillaries 1805, collapse due tosurface tension. Then, the cane is, again, over-clad with a further,thick silica cladding tube (not shown) and is heated and drawn intooptical fiber in a known way. If surface tension alone is insufficientto collapse any of the interstitial voids, a vacuum may be applied tothe interstitial voids, either or both during drawing of the stack intoa cane or the cane into the fiber, for example according to the processdescribed in WO 00/49436 (The University of Bath).

FIG. 20 a is a photograph, taken by the present inventors through amicroscope, of a rod fused to a large diameter capillary before thecapillary is introduced into a pre-form stack. Whether the rod becomes abead along a core boundary, for example as in structures S1, S4, S8 orS9, or a relatively more pronounced nodule protruding only from one sideof a core boundary, for example as shown in FIGS. 15 a-15 c, can becontrolled by the fiber drawing conditions. For example, hotter drawingconditions under lower tension permit a rod and boundary to fusecompletely, thereby forming a bead. In contrast, a colder draw underhigher tension prevents complete fusing of the rod and core boundary,leaving the rod as a nodule on the surface of the core boundary in afinal fiber structure. Clearly, a nodule can be arranged to form on aninner or outer periphery of a core boundary, depending on whether therespective rod is positioned on an inner or outer periphery of a largediameter capillary of the pre-form stack. The properties of a finalfiber structure are expected to vary with bead and/or nodule size andplacement.

FIG. 20 b is an SEM image of a bead, which forms part of a PBG claddingstructure according to an embodiment of the present invention. As shown,the bead has formed along a relatively shorter vein of the claddingstructure. The structure is a result of heating and drawing a preformcontaining the rod shown in FIG. 20 a. The drawing conditions included aheating temperature of about 2050° C., a draw speed of about 2 ms⁻¹ anda draw tension of about 240 g. Clearly, the rod has fused completelywith the capillary under these drawing conditions. It is expected thatcooler and/or faster drawing conditions would lead to the formation of anodule on the inner surface only of the capillary.

An alternative method of forming a pre-form stack 2100, which results inbeads on shorter boundary veins only, is illustrated in FIG. 21.Generally, the stack 2100 comprises the same arrangement of claddingcapillaries 2105, and a large diameter capillary, as stack 1900. In thisexample, however, the larger interstitial voids 2130, which form betweenevery other one of the innermost capillaries and the large diametercapillary 2115, are packed with a glass rod 2140 and two thin-walledcapillaries 2145, which act to hold the glass rod 2140 in a centralposition in the void during drawing down into a cane. Unlike in stack1900, the rods 2140 and capillaries 2145 are not fused to the largediameter capillary 2115 before it is introduced to the stack 2100.Rather, they are introduced into the stack during assembly thereof. Whenthe stack 2100 is heated and drawn down, the rods 2140 form beads on theshorter boundary veins and the thin-walled capillaries collapseentirely—if necessary with the application of a vacuum—adding aninsignificant amount of material to the overall structure.

The pre-form stack of FIG. 21 may be modified slightly as shown in FIG.22, whereby the thin-walled capillaries 2145, on either side of theglass rods 2140, are replaced by additional glass rods 2250. The effectis that, when the stack is drawn down to a fiber, the three glass rodsin each void increase the overall thickness of the associated boundaryvein, whereby thicker boundary veins are created, as in the structuresin FIG. 15 d.

Thicker boundary veins may alternatively be formed in accordance withthe pre-form stack 2300 shown in the diagram in FIG. 23. While thecladding capillaries are arranged in the same way as in previouslydescribed stacks, the inner region of the stack 2300 is formed using twoconcentric, slightly different sized, large diameter capillaries, 2315and 2316. The larger of the large diameter capillaries supports thecladding capillaries, while the smaller of the large diametercapillaries fits within the larger one. The smaller large diametercapillary is sufficiently small that relatively small rods 2340 andcapillaries 2345 can fit in the space between the larger and smallerlarge diameter capillaries.

When the stack 2300 is heated and drawn down into a cane and a fiber,the rods 2340 become thicker boundary veins and the capillaries 2345collapse to form part of the thinner boundary veins.

Thicker boundary veins may alternatively be produced by pre-profiling alarge diameter capillary 2415, for example by using an etching process.First, as shown in FIG. 24 a, a masking agent 2410 is applied to a largediameter capillary 2415 in positions which correspond to requiredregions of increased thickness in a final fiber structure. The maskingagent 2410 is one which inhibits etching by HF, for example apolymer-based photo-resist or a noble metal-based material. According toFIG. 24 b, the capillary is subjected to a flow of HF in an MCVD lathe(in a known manner), whereby the unmasked capillary surfaces 2420 areetched away to the degree required. Finally, the mask is removed and, asshown in FIG. 24 c, the capillary 2415 is used in a capillary stack2400, in which the thicker regions of the capillary 2415 are alignedwith the regions of the stack where thicker boundary veins are required.Of course, masking and etching may selectively be applied to innerand/or outer surfaces and regions of the capillary depending of therequired final form of the capillary.

Alternatively, a core boundary may comprise a predominantly thick-walledcore boundary (not shown) around which relatively short regions ofmaterial have been etched away. This is in contrast to the thin-walledboundary with a number of relatively short thicker regions. A similar,predominantly thick-walled core boundary may be made in a differentmanner by heating and ‘pinching’ regions of a large diameter capillaryprior to it being inserted into a capillary stack. Pinched regions ofthe capillary would form relatively short, thinner regions in a finalcore boundary, and addition of several appropriately-placed pinches maybe used to fine-tune the resulting fiber structure. The capillary couldbe pinched between two elongate tungsten blades, one on the inside ofthe capillary and the other aligned with the first on the outside, forexample, while the capillary is hot enough to be deformed.

An alternative method for forming a capillary stack 2500, which does notrequire a large diameter capillary, is illustrated in FIG. 25. A largediameter capillary is omitted and an insert 2515 is used instead; forexample made of graphite, platinum, tungsten or a ceramic material,which has a higher melting point than silica glass and, preferably, ahigher coefficient of thermal expansion.

The insert 2515 is shaped, by having detents, to support claddingcapillaries and rods and also to support additional glass rods 2510,which eventually become pronounced beads 150.

The stack 2500, including the insert 2515, is heated to allow thecapillaries and rods to fuse into a pre-form. The pre-form is thenallowed to cool and the insert 2515 is removed. It will be apparentthat, at this point, the inwardly-facing walls of the innermostcapillaries take on the general shape of the insert 2515. An advantageof using an insert material having a higher coefficient of thermalexpansion than silica is that, when the pre-form and insert are heated,the insert expands and, relatively-speaking, increases the area of thecentral region in which the insert is located. When permitted to cooldown again, the insert shrinks back down to its original size and thesilica solidifies before shrinking fully back down, leaving an innerregion that is larger than the insert. The insert 2515, which, as aresult, is loose-fitting in the central region, may then be removedreadily from the pre-form with reduced risk of damaging or contaminatingthe pre-form 2500. The resulting pre-form is then heated and drawn inthe usual way, in one or more drawing steps.

A further alternative way to form the fiber is by using a processsimilar to that described in PCT/GB00/01249, wherein the claddingcapillaries and rods, and additional capillaries and/or rods for shapingthe boundary, are supported by truncated capillaries at either end ofthe stack. The stack may be drawn to an optical fiber in the normal way,and the parts of the fiber incorporating the truncated capillarymaterial may be discarded. In principle, truncated capillaries may alsobe used to support the stack part way along its length.

The diagram in FIG. 26 illustrates a small portion of an outer region ofa pre-form stack 2600 made from circular cross section capillaries 2620.In this embodiment, the entire stack is contained in a large circularcross section capillary tube 2670, having a generally circular bore,which is large enough to receive the entire assembled stack as a slidingfit. As shown, interstitial voids 2675 form between the edges of thestack and the internal surface of the large capillary. It has been foundbeneficial to pack these interstitial voids with circular cross sectionpacking rods 2680, having various sizes selected to support all claddingcapillaries in their appropriate positions within the large capillary.These rods melt and fuse with the large circular capillary to form ahomogenous outer layer of glass that surrounds the microstructured innerregion.

FIG. 32 is a diagram of a transmission system 3200 comprising an opticaltransmitter 3210, an optical receiver 3220 and an optical fiber 3230between the transmitter and receiver. The optical fiber 3230 comprisesalong at least a part of its length an optical fiber according to anembodiment of the present invention. Other components or systems, forexample to compensate for dispersion and loss, would typically beincluded in the system but are not shown in FIG. 32 for the sake ofconvenience only.

The following examples of different structures closely resemblepractical optical fiber structures, which have either been made by thepresent inventors or may be made according to known processes or theprocesses described hereinafter. The exemplary structures share thefollowing common characteristics:

a pitch Λ of the cladding chosen between values of approximately 3 μmand 6 μm (this value may be chosen to position core-guided modes at anappropriate wavelength for a particular application);

a thickness t of the cladding veins of about 0.06 times the chosen pitchΛ of the cladding structure (or simply 0.0586Λ);

an AFF in the cladding of approximately 91%; and

a ratio R having a value of about 0.6.

For other features and parameters referred to in the following,reference is made to FIGS. 1 and 2 and the discussion above.

In particular, a figure of merit, identified herein as F-factor, is usedby the present inventors as a measure of the degree to which the guidedlight propagating in a PBG fiber is subject to scattering from smallscale irregularities of the air-silica interfaces. F-factor is alsobelieved to be a strong indicator of likely mode-couplingcharacteristics of a PBG-fiber. The most relevant F-factor is typicallythe F-factor only of the mode of interest (for example, the fundamentalmode, ignoring higher-order modes).

Scattering due to small scale irregularities acts in addition to theRayleigh scattering due to index inhomogeneity within silica, or anyother such optical guiding medium. The latter loss mechanism is stronglysuppressed in air-core PBG fibers, if most of the light power is in air.It remains to ascertain the limit that hole interface scattering placeson loss, given that some interface roughness is always present. Theamount of scattering associated with air-silica boundaries can beminimised by ensuring that impurities are eliminated during the drawprocess; such impurities can act as scattering (and absorption) centersdirectly, and can operate as nucleation sites for crystallite formation.With these imperfections removed, there still remains interfaceroughness governed by the thermodynamics of the drawing process. Theinventors believe that such fluctuations are likely to be difficult orimpossible to remove altogether.

The Rayleigh scattering due to small scale roughness at the air-silicainterfaces may be calculated by applying a perturbation calculation. Theanalysis has a simple interpretation in terms of effective particulatescatterers distributed on the interfaces. If the root-mean square (RMS)height roughness is h_(rms) and the correlation lengths of the roughnessalong the hole direction and around the hole perimeter are L_(z) andL_(□) respectively, then a typical scatterer has a volumeh_(rms)L_(z)L_(φ). The induced dipole moment of the typical scatterer isthen given by

p=Δ∈E₀h_(rms)L_(z)L_(φ)  (2)

where Δ∈ is the difference in dielectric constant between silica andair, and E₀ is the E-field strength at the scatterer. This induceddipole moment radiates a power, in the free space approximation, givenby

$\begin{matrix}\begin{matrix}{P_{sc} = {\frac{1}{12\; \pi}( \frac{\omega}{c} )^{4}( \frac{ɛ_{0}}{\mu_{0}} )^{1/2}{p}^{2}}} \\{= {\frac{1}{12\; \pi}( \frac{\omega}{c} )^{4}\Delta \; ɛ^{2}h_{rms}^{2}L_{z}^{2}{L_{\varphi}^{2}( \frac{ɛ_{0}}{\mu_{0}} )}^{1/2}{{E_{0}}^{2}.}}}\end{matrix} & (3)\end{matrix}$

The number density of particles on the interface will be ˜1/(L_(z)L_(φ))so that the total radiated power from a section of length L of theperturbed fiber will be approximately

$\begin{matrix}{P_{rad} \sim {\frac{1}{12\; \pi}( \frac{\omega}{c} )^{4}\Delta \; ɛ^{2}h_{rms}^{2}L_{z}L_{\varphi}{L( \frac{ɛ_{0}}{\mu_{0}} )}^{1/2}{\oint\limits_{{hole}\mspace{14mu} {perimeters}}{{s}{E_{0}}^{2}}}}} & (4)\end{matrix}$

The loss rate is thus given by

$\begin{matrix}{\gamma = {\frac{P_{rad}}{P_{0}L} \sim {\frac{1}{6\; \pi}( \frac{\omega}{c} )^{4}\Delta \; ɛ^{2}h_{rms}^{2}L_{z}{L_{\varphi}( \frac{ɛ_{0}}{\mu_{0}} )}^{1/2}\frac{\oint\limits_{{hole}\mspace{14mu} {perimeters}}{{s}{E_{0}}^{2}}}{\int{{{S( {E_{0}\bigwedge H_{0}^{*}} )}} \cdot \hat{z}}}}}} & (5)\end{matrix}$

where the incident power P₀ has been expressed as a Poynting flux.

Equation (5) shows that the mode shape dependence of the Rayleighinterface roughness scattering strength is governed by an F-factor,given by

$\begin{matrix}{F = {( \frac{ɛ_{0}}{\mu_{0}} )^{1/2}{\frac{\oint\limits_{{hole}\mspace{14mu} {perimeters}}{{s}{{E_{0}( r^{\prime} )}}^{2}}}{\int_{x\text{-}{section}}\ {{{S( {E_{0}\bigwedge H_{0}^{*}} )}} \cdot \hat{z}}}.}}} & (6)\end{matrix}$

For values stated herein, F-factor has units of Λ⁻¹. The lower theF-factor is, the less interaction there is between light and air/glassinterfaces and the lower the degree of scattering and mode coupling is.Embodiments of the present invention are intended to have reducedF-factor compared with prior art fibers.

The inventors have found that a comparison of the interface scatteringstrength from guided modes of different fibers with similar interfaceroughness properties can be based purely on the F-factor. Indeed, thethermodynamic limit to surface roughness is not expected to vary greatlywith small variations in the fiber geometry, so that the F-factor can beused directly as a figure of merit for any fiber which has interfaceswhich cause scattering and contribute to loss.

The F-factor of a particular structure can also be measured indirectlyfor a real fiber structure by the following method. A SEM or atomicforce microscopy (AFM) image is taken of the cross-sectional structureof the fiber in question. An accurate representation of the structure,suitable for use in computer modelling, is obtained from the image byestimating the position of the structural boundaries throughout thecross-section. Based on this representation, the mode field can besimulated by solving Maxwell's vector wave equation for the fiberstructure, using known techniques, as already described. Knowledge ofthe electric and magnetic field distributions enables both the numeratorand denominator in Equation (6) above to be calculated.

The very small size of the thin veins in the structure means that greatcare must be taken when interpreting an SEM image. The apparentthickness of a vein in the image may be slightly different from the truethickness, but the small discrepancy will have a large impact on theF-factors determined from it. It is therefore advisable to confirm thevalidity of the process by which the model structure is determined fromthe SEM image, to yield a reliable fit. One way to confirm the fit wouldbe through spectral measurements of the loss of the fiber, which oftenshow peaks at particular wavelengths due to mode crossings [see, forexample, Smith et al., “Low-loss hollow-core silica/air photonic bandgapfiber”, Nature, Vol. 424 pp 657-659, 7 Aug. 2003].

In arriving at the present invention, the present inventors haveanalysed the performance of various fiber structures, which aregenerally similar to the structure shown in FIG. 1. The structuresanalysed herein, however, differ from one other and from the structurein FIG. 1 by having different sizes and shapes of bead around the coreboundary.

The different bead types described herein are illustrated schematicallyin the diagrams in FIG. 27. In FIG. 27, there are nine beads types,labelled S1 to S9. Beads S1 to S9 have the aspect ratios shown as (minordimension: major dimension). Beads S1 to S5 have in common the samecross-sectional area and beads S6 to S8 have in common the same aspectratio. Also, beads S1 and S6 share the same major dimension, which isshown in FIG. 3 as a fraction 0.288 of the pitch, or 0.288Λ. Beads S2and S3 share the same identified major dimensions with beads S7 and S8respectively.

Bead S9 is an exception to the others in that it is arranged to begenerally representative of the prior art beads, having an aspect ratioof 1:3 and a major dimension which is just over 0.4Λ. The form of theprior art bead S9 was established by carefully measuring the relativelylow resolution images in the respective prior art scientific papers.

In all fiber structures analysed herein, the beads are located midwayalong every other one of the longer boundary veins, which are associatedwith the pentagonal boundary cells; similar to the beads shown in thediagram in FIG. 1. That is, each fiber structure has six beads aroundthe core boundary, which encloses a seven cell core defect, and thebeads are substantially the same in any given structure. While otherkinds of structures are not described in detail herein, the presentinventors believe that similar principles of bead-type selection willapply to other forms of structure, for example a nineteen cell coredefect structure, and the skilled person, on reading the presentdescription, will be able to analyse a broad range of bead sizes andtypes with different kinds of fiber structure.

The relative form of the beads S1 to S9 is shown on the graph in FIG.28, which plots minor dimension against major dimension, both in unitsof pitch Λ.

The graph in FIG. 29 plots F-factor against normalised propagationconstant K (2πΛ/λ) for structures S1 to S5, which share in common thesame area. As shown in the graph, the values for F-factor varysignificantly for each structure with varying wavelength. The peaks ineach plot are believed to be due to mode crossings. The subject of modecrossings is beyond the scope of the present description. However, thereader is referred to papers, such as the aforementioned paper “Surfacemodes and loss in air-core photonic band-gap fibers”, for a moredetailed analysis of mode crossings.

A clear trend apparent from the graph in FIG. 29 is that, for a givenbead area, F-factor decreases with decreasing aspect ratio. In otherwords, the F-factor appears to be at a highest level when the beads aresubstantially round (S1) and tends to decrease in value as the beadsbecome more elongate. The fiber structure having beads of the form of S5clearly has the best F-factor characteristics and is, therefore,expected to produce a low loss transmission fiber.

A similar graph is plotted in FIG. 30 for structures S2, S7 and S9,which share in common a major dimension of 0.408Λ. FIG. 30 clearly showsthat, for a given major dimension, F-factor decreases with decreasingaspect ratio, with a fiber having beads of the form of S7 exhibiting thelowest F-factor characteristics.

A summary of lowest achieved F-factor for fiber structures having eachkind of bead is illustrated in the graph in FIG. 31, and summarised inthe following table 4. Each structure is represented by a circle on thegraph, where the diameter of each circle represents the respectivelowest F-factor.

TABLE 4 Minor Major Aspect Lowest Bead dimension/

dimension/

Ratio F-factor Constant Area S1 0.288 0.288 1.00 (1:1) 0.359 S2 0.2040.408 0.50 (1:2) 0.132 S3 0.167 0.500 0.33 (1:3) 0.098 S4 0.144 0.5770.25 (1:4) 0.090 S5 0.096 0.866 0.11 (1:9) 0.075 Constant Ratio S6 0.0720.288 0.25 (1:4) 0.183 S7 0.102 0.408 0.25 (1:4) 0.085 S8 0.125 0.5000.25 (1:4) 0.088 Prior Art S9 0.136 0.408 0.33 (1:3) 0.101

Even though the graph in FIG. 31, and the values in the table, do notrepresent the variation in F-factor across the waveband, the lowestF-factor values do represent their respective general trends (shown inthe graphs in FIGS. 29 and 30) and so do provide a valid indication oflikely relative performance of the various structures.

It is clear that the prior art beads perform better, in terms ofF-factor, than a number of the other bead forms. For example, beads S1,S2 and S6, have relatively high associated F-factors and would beunlikely to perform as well as S9 in a practical fiber. In contrast,beads S3, S4, S5, S7 and S8, have varying degrees of improved (lower)F-factor, compared with S9, where S3 exhibits only a marginalimprovement and S5 exhibits an extremely significant improvement. Inother words, a fiber structure incorporating beads such as S5 is likelyto produce a lower loss fiber than a prior art fiber incorporating beadssuch as S9.

In practical optical fiber transmission systems, it is expected that onefixed parameter will be operating wavelength. It is well-known that aPBG fiber can be designed for operation at a given wavelength, forexample at around 1550 nm, since the dimensions of PBG structures simplyscale with wavelength. However, the present inventors anticipate thatthere may be a need to tune a given PBG fiber structure, to optimise itsperformance at the given wavelength; for example, by manipulating thespectral positions of surface modes to move them away from the coremodes of interest. Embodiments of the present invention are expected tofind particularly beneficial application as a way of so tuning PBGfibers, independently or in addition to varying core diameter and otherparameters of the fibers. This belief is supported by the graphs inFIGS. 29 and 30, where mode crossing peaks clearly move around thespectrum as a result of changing only the form of the beads.

With reference to FIG. 17, prior art structures of the kind exemplifiedin FIG. 1 may be made from a pre-form 1700 comprising a stack ofhexagonal capillaries 1705. The hexagonal capillaries 1705 each have acircular bore. The cladding nodes 160 and boundary nodes 150 (fromFIG. 1) of the PBG fiber structure result from the significant volume ofglass that is present in the preform 1700 wherever the corners 1710,1715 of neighboring capillaries meet. The beads 165 are formed from theglass of the inwardly-facing corners 1720 of the capillaries that boundan inner region 1725 of the pre-form 1700, which is to become the coredefect region 110 (cf. FIG. 1) of a PBG fiber structure. These corners1720, and the two sides of each capillary that meet at the corners,recede due to surface tension as the stack of capillaries is heated anddrawn. Such recession turns the two sides and the corner 1720 into aboundary vein 140, with a bead 165. The inner region 1725 may be formedby omitting the inner seven capillaries from the pre-form and, forexample, supporting the outer capillaries using truncated capillaries ateither end of the stack, as described in PCT/GB00/01249 (describedabove) or by fusing a complete stack of capillaries together and thenetching away glass from inner capillaries in accordance with either ofthe processes described in PCT/GB00/01249 or U.S. Pat. No. 6,444,133. Insome prior art structures, it is believed that the beads may result froman etching process rather than being entirely due to use of hexagonalcapillaries. In either event, though, the beads are merely an artefactof the process used to make the fiber, rather than being an intentionalfeature of the final structure.

While it may be possible to adapt prior art processes for making fibersaccording to embodiments of the present invention, in which bead sizeand shape are selectively varied, the present inventors believe it wouldbe difficult. For example, it would be difficult to adapt the preform inFIG. 17 to produce larger or more elongate beads than those shown inFIG. 1, without interfering with one or more other characteristics ofthe fiber. In general, formation of different sizes and shapes of beadsor nodules (or the like) at selected locations around the core boundaryis likely to be difficult using prior art processes.

The diagram in FIG. 19 illustrates one way of forming a pre-form stack1900, including a seven cell core region 1910, which is suitable forforming a PBG fiber structure according to embodiments of the presentinvention. The core region 1910 is formed by assembling circular crosssection capillaries 1905 in a close-packed triangular arrangement arounda large diameter core capillary 1915, which is large enough to supportcapillaries around a region left by removal of seven capillaries: aninner capillary and the six capillaries around the inner capillary. Thelarge diameter core capillary 1915 supports the cladding capillarieswhile the stack is being formed and eventually becomes part of thematerial that forms a core defect boundary.

Interstitial voids 1920 that form at the mid-point of each close-packed,triangular group of three cladding capillaries are each packed with aglass rod 1925. The rods 1925 that are packed in the voids assist informing cladding nodes, which have a diameter d that is typicallysignificantly greater than the thickness t of the veins that meet at thenodes. Omission of a rod from a void in the cladding leads to theformation of a cladding node that has a relatively smaller diameter, forexample closer to the thickness of the respective adjoining veins.

The rods 1925 may be inserted into the voids after the capillaries havebeen stacked. Alternatively, the stack may be assembled layer by layer,with the rods that rest on top of capillaries being supported by anappropriate jig, for example positioned at either end of the stack,until the next upper layer of capillaries is in place to support thoserods. In commercial scale operations, it is apparent that the manualtask of forming a pre-form stack could readily be automated, usingappropriately programmed robots, for example of the kind used incomponent laying for printed circuit boards.

The interstitial voids 1930 that are formed between the claddingcapillaries 1905 and the large diameter capillary 1915 are not packedwith any rods, thereby minimising the volume of glass that is available,during drawing of the stack 1900, for formation of boundary nodes.

As shown in FIG. 19, the large diameter capillary 1915 has attached toits inner surface twelve silica rods 1935. The rods 1935 are fused tothe inside of the large diameter capillary 1915 in an additional heatingstep before the capillary is introduced to the stack 1900. When thestack 1900 is heated and drawn into fiber, these rods fuse with thelarge diameter capillary 1915, which itself fuses to the inwardly facingsurfaces of the innermost cladding capillaries, to form core boundarybeads of the kind described herein. The rods 1935 can be selectivelypositioned on the inside of the large diameter capillary 1915 to bealigned with either or both of the longer or shorter core boundaryveins. Of course, within practical limits, any number of rods 1935 maybe attached to the inside, or indeed outside, of the large diametercapillary 1915. If attached on the outside of the large diametercapillary 1915, the rods may be aligned with the larger interstitialvoids 1930. Of course, the size of the bead required in the fiberstructure dictates the selected diameter of the respective rod 1935.

In principle, rods 1935 may be attached to the inside or to the outsideof the large diameter capillary 1915. Indeed, rods may in principle beattached to both the inside and the outside of the same region of thelarge diameter capillary 1950, so that they form a relatively largerbead on the core boundary.

The pre-form stack 1900 is arranged as described with reference to FIG.19 and is then over-clad with a further, relatively thick-walledcapillary, which is large enough to contain the stack and small enoughto hold the capillaries and rods firmly in place. The entire over-cladstack is then heated and drawn into a so-called cane, during which timeall the relatively large interstitial voids 1930 and any remaining voidsbetween the glass rods and the cladding capillaries, collapse due tosurface tension. Then, the cane is, again, over-clad with a further,thick silica cladding tube and is heated and drawn into optical fiber ina known way. If surface tension alone is insufficient to collapse any ofthe interstitial voids, a vacuum may be applied to the interstitialvoids, either or both during drawing of the stack into a cane or thecane into the fiber, for example according to the process described inWO 00/49436 (The University of Bath).

FIG. 20 a is a photograph, taken by the present inventors through amicroscope, of a rod fused to a large diameter capillary before thecapillary is introduced into a pre-form stack. The shape of theresulting bead can be controlled by the fiber drawing conditions. Forexample, hotter drawing conditions under lower tension permit a rod andboundary to fuse completely, thereby forming a more elongate bead. Incontrast, a colder draw under higher tension forms a bead with a shortermajor dimension.

FIG. 20 b is an SEM image of a bead along the core boundary of a fiber.The structure is a result of heating and drawing a preform containingthe rod shown in FIG. 10 a. The drawing conditions included a heatingtemperature of about 2050° C., a draw speed of about 2 ms⁻¹ and a drawtension of about 240 g. Clearly, in order to form a bead of the kindillustrated by S3, S4 or S5, it would be necessary to use a rod (orrods) having a greater cross section area.

An alternative method of forming a pre-form stack 2100, which results inbeads on shorter boundary veins only, is illustrated in FIG. 21.Generally, the stack 2100 comprises the same arrangement of claddingcapillaries 2105, and a large diameter capillary, as in stack 1900 ofFIG. 19. In this example, however, the larger interstitial voids 2130,which form between every other one of the innermost capillaries and thelarge diameter capillary 2115, are packed with a glass rod 2140 and twothin-walled capillaries 2145, which act to hold the glass rod 2140 in acentral position in the void during drawing down into a cane. Unlike instack 1900, the rods 2140 and capillaries 2145 are not fused to thelarge diameter capillary 2115 before it is introduced to the stack 2100.Rather, they are introduced into the stack during assembly thereof. Whenthe stack 2100 is heated and drawn down, the rods 2140 and thin-walledcapillaries, which collapse entirely (if necessary with the applicationof a vacuum), form elongate beads on the shorter boundary veins. Suchbeads can resemble those illustrated by S5 or S8. In principle, asimilar arrangement of rods and thin-walled capillaries may be fused tothe inner surface of a large diameter capillary, in the event theresulting beads are to be positioned along the longer boundary veins.

A further alternative way to form the fiber is by using a processsimilar to that described in PCT/GB00/01249, wherein the claddingcapillaries and rods, and additional capillaries and/or rods for shapingthe boundary, are supported by truncated capillaries at either end ofthe stack. The stack may be drawn to an optical fiber in the normal way,and the parts of the fiber incorporating the truncated capillarymaterial may be discarded. In principle, truncated capillaries may alsobe used to support the stack part way along its length.

FIG. 32 is a diagram of a transmission system 3200 comprising an opticaltransmitter 3210, an optical receiver 3220 and an optical fiber 3230between the transmitter and receiver. The optical fiber 3230 comprisesalong at least a part of its length an optical fiber according to anembodiment of the present invention. Other components or systems, forexample to compensate for dispersion and loss, would typically beincluded in the system but are not shown in FIG. 32 for the sake ofconvenience only.

The structure in FIG. 1 and each of the following examples of differentstructures closely resemble practical optical fiber structures, whichhave either been made or may be made according to known processes or theprocesses described hereinafter. The structures share the followingcommon characteristics:

a pitch Λ of the cladding chosen between values of approximately 3 μmand 6 μm (this value may be chosen to position core-guided modes at anappropriate wavelength for a particular application);

a thickness t of the cladding veins of 0.0548 times the chosen pitch Λof the cladding structure (or simply 0.0548Λ);

an air-filling fraction (AFF) in the cladding of approximately 87.5%.

For other features and parameters referred to in the following,reference is made to FIGS. 1 and 2 and the discussion above.

The present inventors have determined that it is possible to control theperformance of PBG fibers in particular by aiming to maximise the amountof light that propagates in air within the fiber structure, even if somelight is not in the core, in order to benefit from the properties of PBGfibers, such as reduced absorption, non-linearity and, in addition,reduced mode coupling.

In particular, the inventors have identified the importance of the shapeof the boundary for controlling the amount of light that propagates inair within the structure and for controlling the F-factor of thestructure.

The core-cladding interface region of an air core PBG waveguide such asa photonic crystal fiber can be designed to exploit an anti-resonanceeffect to enhance the fraction of the mode power which resides in air.The geometry giving rise to the anti-resonance discussed here is basedon a number of substantially localized regions of silica (nodules 165)placed on the core surround.

As described above, FIG. 1 shows examples of locally concentrated highindex regions (nodules 165) encircling an air core 110. Thin silicaveins or struts 130, 140 connect the nodules together. Those strutsdirectly connect onto to the PBG cladding region. If the strutsconnecting the concentrated regions of silica are thin, having athickness less than 0.15 times the operational wavelength λ (which theyare in the case of FIG. 1), then the struts 130, 140 connecting thelocalized high index regions do not themselves induce an anti-resonanceeffect; the anti-resonance is associated with substantially isolatedhigh index regions 165. Indeed, it is found that localized regions ofhigh index on a thin core surround can confine light better than acontinuous core surround which possesses an approximately even densityof silica, although alternatively a continuous core surround can beoptimised, as described in co-pending International Patent Application.

The fiber of FIG. 1 has a structure similar to structures disclosed inseveral prior art publications, for example, “Low Loss (13 dB/km) AirCore Photonic Bandgap Fiber”, Venkataraman et al., Proc. ECOC 2002,Copenhagen; “Interferometric Chromatic Dispersion Measurement ofPhotonic Band-gap Fiber”, Mueller et al., Proc. SPIE 2002, Vol. 4870,Boston; “Photonic Crystal Fibers”, West et al., Proc. ECOC 2001, paperThA22, Vol. 4, Amsterdam; and “Photonic Crystal Fibers: Effective-Indexand Band-Gap Guidance”, Gallagher et al., Photonic Crystals and LightLocalization in the 21^(st) Century, pp. 305-320, Kluver (ISBN0-7923-6947-5); “Dispersion and nonlinear propagation in air-corephotonic band-gap fibers”, Ouzounov, Ahmad, Gaeta, Müller, Venkataraman,Gallagher, Koch, CLEO 2003. The nodules present in those structuresappear to be artefacts of the process used to manufacture the waveguidesdescribed. None of the prior art documents attach any significance tothe features and there is no suggestion that the features exhibit anyantiresonance effect. Moreover, the present inventors have investigatedthe structures disclosed in those prior art documents and have foundnothing to suggest that those structures exhibit antiresonance:generally the nodules appear to be too small. However, the inventorshave discovered that structures similar to the prior art structures doexhibit beneficial antiresonance effects. The inventors have discoveredthat presence or absence of these effects is very sensitive to thegeometry of the structure, such as the dimensions of the nodules.Investigations by the inventors suggest that the described prior artstructure has nodules with L in the range 0.27Λ to 0.45Λ and W in therange 0.11 Λ to 0.21Λ; however, calculation of those values is based onan analysis of the SEM images in the prior art documents and theaccuracy of the analysis is dependent upon the quality of those images.Those prior art structures, be they corresponding to those ranges orotherwise, are hereby disclaimed.

The mechanism by which anti-resonance due to localized regions of highindex can occur may be understood by considering a corral of high indexcylinders distributed around a closed loop, which may or may not be acircle. Examples of such a geometry are shown in FIG. 33. The cylindersare everywhere surrounded by air. This system may be analysed quicklyand accurately by employing a multiple scattering approach which fullyexploits Mie-scattering theory; the field scattered from each cylinderis expanded in a multipole series. By applying the electromagneticboundary conditions at the surfaces of the cylinders, an eigenvalueequation is derived. The method invokes radiating boundary conditionsand can readily calculate leaky modes as well as guiding modes of thesystem; the former are obtained as solutions with complex β-values, withβ the wavevector component along the direction of a cylinder axis. Theguided modes, which are concentrated in the cylinders, satisfyRe[β]>ω/c, Im[β]=0. Only leaky modes with small imaginary P components,and which therefore leak only slowly, are retained; leakage rate isproportional to Im[β]. Re[β] for the leaky mode solutions lies close toand just below the air light-line value ω/c.

A corral system, such as any of the examples shown in FIG. 33, is foundto support an LP₀₁-like leaky mode solution, which possesses anapproximately Gaussian intensity profile centered at a point p in theair region which is enclosed by the corral arrangement. Those solutionsexist close to the air light line, β=ω/c, so that the cylinders have astrong influence on the field. The cylinders force near nulls in thefield intensity to occur close to their boundaries. For a given cylinderarrangement, by adjusting the size of the cylinders, the near nulls canbe placed very close to the positions on the cylinder boundaries whichlie closest to the point p. It is observed that Im[β] of the leaky modesolution is minimised when this occurs, meaning that the leakage rate isminimised. That is interpreted as an anti-resonance of the corralsystem; anti-resonances of more simple confining systems such as adielectric ring are also signalled by a near-null occurring very closeto the innermost dielectric interface. FIG. 34( c) plots Im[β] againstthe cylinder diameter d for 6 cylinders evenly spaced around a circle(FIG. 34( a)), with circle radii R=3.0, 4.5 and 6.0 μm. (As is wellknown, the imaginary part of a refractive index corresponds physicallyto loss in the medium.) Also shown is Im[β] for a circular silica ringagainst its thickness d, for a ring radius of R=4.5 μm (FIG. 34( b)).The wavelength was set to λ=1.55 μm. The superior confinement ability ofthe cylinder corral system at Λ=4.5 μm is clearly observed.

The confining ability of a corral system is very dependent on the numberand the location of the high index regions. If the regions are too farapart, such that for the LP₀₁-like leaky mode solution |√{square rootover ((ω/c)²−β²)}|d exceeds approximately π, with d the largestseparation of neighboring high index regions in the corral, confinementwill be weak. That is because the mode can resolve one or more of thegaps between the high index regions and so escape. That resolutionargument can also be invoked to explain why the corral system supportsfar fewer leaky modes than a continuous element such as a dielectricring. The in-plane wavevector associated with higher order modes exceedsthat of the more slowly varying LP₀₁-like mode, so that in the corralsystem, the higher order modes are more able to resolve the gaps betweenthe high-index regions and leak away. This is an advantage of the corralsystem over the continuous design; the latter will generally supportmore modes within and nearby the band gap region and will therefore bemore subject to mode coupling loss.

Optimum confinement induced by a number of identical, parallelhigh-index cylinders in a corral geometry is achieved when the cylindersare evenly spaced over the circumference of a circle. The optimum numberof cylinders to place around the circle depends on its radius R. Thewidth of the anti-resonance as a function of parameters such as cylinderradius or wavelength is increased by including more cylinders, butincreasing the number of cylinders beyond a certain number will weakenthe confinement that can be achieved.

Although the circular corral arrangement of cylinders is optimum, theLP₀₁-like leaky mode is able to accommodate significant movement incylinder positions without incurring much increase in loss; the fieldassociated with this mode redistributes itself to move the near nulls ofthe field so that they remain close to the cylinder boundaries. The losspenalty incurred by the movement is small as long as the area of theregion existing within the corral exceeds ˜10λ² and the separation ofneighboring cylinders remains below the resolution capacity of the mode.FIGS. 35 (a) and (b) shows the field intensity distribution for twodifferent arrangements of 12 identical silica cylinders. In each case,the radius of the cylinders was chosen to correspond to anti-resonance.The maintenance of the positions of nulls close to the cylinderboundaries is clearly observed. FIG. 36 compares the confinement abilityof the two arrangements of 12 cylinders as a function of the cylinderdiameter d. The difference in the confinement ability of the twogeometries is not severe. The confinement of the 12 cylinders evenlydistributed around the hexagon, shown in FIG. 35( b), is found to bevirtually identical with 12 cylinders distributed evenly around a circlewith an area equal to that of the hexagon.

As described above, the present inventors have determined that it ispossible to control the performance of PBG fibers in particular byminimising the F-factor or maximising the amount of light thatpropagates in air within the fiber structure, even if some light is notin the core, in order to benefit from the properties of PBG fibers, suchas reduced absorption, non-linearity and, in addition, reduced modecoupling. The present inventors use light power in air and F-factor asproxies to anti-resonance exhibited by the core boundary.

Corral systems comprising parallel elongated elements with differentshapes in cross-section, such as ellipses, will behave similarly to thecylinder case described above. The confining ability of theanti-resonance will depend upon the shape and orientation of theelements; shapes with smooth surfaces with no locally high rates ofcurvature can be expected to induce better confinement than shapes whichpossess sharp features on their surfaces. Numerical simulations of aircore PBG fibers which incorporate concentrated high index regionslocated around the core surround have shown that the corralanti-resonance effect remains present even in such a complex geometry.As a function of a parameter such as the size of the concentrated highindex regions, broad maxima are observed in the power in air fraction ηand broad minima appear in the factor F given by, Eqn. 7

$\begin{matrix}{F = {( \frac{ɛ_{0}}{\mu_{0}} )^{1/2}\frac{\oint\limits_{{hole}\mspace{14mu} {perimeters}}{{s}{E_{0}}^{2}}}{\int_{x\text{-}{section}}\ {{{S( {E_{0}\bigwedge H_{0}^{*}} )}} \cdot \hat{z}}}}} & (7)\end{matrix}$

The quantity F measures field intensity at the dielectric interfaces andgives a direct relative measure of the strength of small-scale interfaceroughness scattering and provides an indication of the relative strengthof mode coupling effects due to longer scale fluctuations. Uponexamination of the LP₀₁-like mode field intensity profile at maximum ηand minimum F, it is observed that near nulls occur close to theboundaries of the concentrated high index regions at locations closestto the position of peak intensity p. That confirms the mechanism inoperation has the character of anti-resonance. The band gap claddingregion can be interpreted as simply completing the confinement of themode, which has already been substantially localized by the corraleffect. Indeed, exploiting a corral anti-resonance can render the fieldintensity everywhere within the cladding to be more than 20 dB below thepeak intensity value. The analysis of the simple cylinder corral systempresented above can be used to estimate the optimum number ofconcentrated elements to place around the core surround, give anindication of the size that these elements should have, and indicate thesensitivity to the parameters. Detailed numerical investigation of PBGphotonic crystal fibers with concentrated index elements around the coresupports this view.

In considering the variation of light in air and F-factor with anyparticular parameter, it should be noted that interactions between themode being investigated and so-called surface modes near to the coreboundary may lead to ghost resonance peaks. This kind of interaction isalso identified in Müller, D. et al. “Measurement of photonic band-gapfiber transmission from 1.0 to 3.0 μm and impact of surface modecoupling.” QTuL2 Proc. CLEO 2003 (2003). This paper supports the presentinventors' view that mode power from the air-guided modes may couple tolossy surface modes, which concentrate in or near to the core boundary.The result is increased loss, attendant increased F-factor and reducedlight in air fraction. Indeed, for the case of a core boundary ofuniform thickness, it is found that such mode crossings are suppressedfor core thicknesses close to the anti-resonant value, but becomeabundant for core thicknesses away from anti-resonance. This surfacemode exclusion property associated with the anti-resonance renders thecurves for F-factor and amount of light in air smoother as they reachoptimum values at core boundary thicknesses close to the anti-resonantpoint.

That an antiresonant core boundary is desirable for reducing the impactand/or number of surface modes in a PBG fiber is surprising andcounter-intuitive, particularly when one considers the prior art, forexample the teachings in the book “Photonic Crystals: Molding the Flowof Light”. From such a reference, the skilled man would understand thatsurface modes can form due to the inclusion of a defect in a PBFstructure; for example a hollow core defect in a PBG fiber. Afterappreciating this, it would appear sensible to include only a singledefect in the structure; where plural defects could lead to plural setsof surface modes. Hence, it would appear reasonable to form a coredefect boundary that, as closely as possible, matches the veins in thecladding structure. Otherwise, the core defect boundary might been‘seen’ by the light as a additional defect, or even a waveguide in itsown right, since it neither matches the core defect nor the cladding. Inother words, having a core defect boundary that is significantlydifferent, for example thicker in transverse cross section, than theindividual cladding veins of the PBG cladding structure, would not havebeen a natural choice for the skilled person who wanted to avoid theformation of surface modes.

In order to remove the ghost resonance peaks, it is either necessary toremove the surface states or adjust the operating point of the waveguideto avoid mode crossings. Moving the operating point for a given geometrycan be achieved by varying the operating wavelength within the band gapand/or adjusting the pitch Λ of the photonic band-gap structure. Clearlythe avoidance of mode crossings facilitated by a core surround close toanti-resonance will typically enable a wider wavelength bandwidth to beof practical use.

The inventors have investigated the effect of varying the size ofnodules 165. To that end, an ellipse may be fitted to the nodule. FIG.37 shows how ellipses are fitted to nodules 165 in a waveguide boundaryregion.

The light power-in-air fraction of a particular structure is directlymeasurable. The method of measuring light power-in-air involves taking anear-field image of light as it leaves the structure, overlaying it onan SEM image of the structure and directly calculating the lightpower-in-air fraction from the overlap of the two images.

The F-factor can also be calculated for a real fiber structure by thefollowing method. A Scanning Electron Micrograph (SEM) is taken of thecross-sectional structure of the fiber in question. An accuraterepresentation of the structure, suitable for use in computer modelling,is obtained from the SEM by estimating the position of the structuralboundaries throughout the cross-section. The mode profile is thencalculated from the estimated structure using a computer modellingscheme described below. This provides knowledge of the electric andmagnetic field distributions which enables both the numerator anddenominator in Equation (5) above to be calculated.

The very small size of the thin veins in the structure means that greatcare must be taken when interpreting an SEM image. The apparentthickness of a vein in the image may be slightly different from the truethickness, but the small discrepancy will have a large impact on thelight power-in-air fraction and F-factors determined from it. It istherefore advisable to confirm the validity of the process by which themodel structure is determined from the SEM image, to yield a reliablefit. One way to confirm the fit would be through spectral measurementsof the loss of the fiber, which often show peaks at particularwavelengths due to mode crossings. [see Smith et al., “Low-losshollow-core silica/air photonic bandgap fiber”, Nature, Vol. 424 pp657-659, 7 Aug. 2003]

The % light in air may also be calculated by superimposing the modelledmode on the modelled structure. FIG. 38 shows an idealised schematic ofa portion of the fiber structure. Once the nodule is represented by anellipse, the nodule is characterised by two parameters, the length L ofthe ellipse's major axis and the length W of its minor axis. In theexample of FIG. 1, the strut width is 0.05477Λ, the length L of thefitted ellipse is 0.5Λ and the length W is 0.5Λ/3.

FIGS. 39 and 40 show how the proportion of light in air and theF-factor, respectively, of mode guided in a fiber having a structure ofthe general form of FIG. 1 varies with the parameters L and W, at anoperating wavelength of 1550 nm. In generating the plots of FIGS. 39 and40, the fiber structure of FIG. 1 was modelled on a computer and theproportion of light in air and the F-factor were calculated for variouscombinations of L and W. Each circle in the plots of FIGS. 39 and 40represents one such combination of L and W; the diameter of the plottedcircle is proportional to the proportion of light power in air orF-factor, with smaller circles representing better performance, that isa higher proportion of light in air or a lower F-factor. The largestcircle in FIGS. 39 and 40, at co-ordinate (4Λ/12,4Λ/36) in each plot,corresponds to a % light in air of 96.7% and an a F-factor of 0.74 Λ⁻¹.The smallest circle in FIGS. 39 and 40, at co-ordinate (5Λ/12,6Λ/36) ineach plot, corresponds to a % light in air of 99.3% and an a F-factor of0.13 Λ⁻¹.

Plots of the kind shown in FIGS. 39 and 40 have been shown to provide areliable means for distinguishing between good and bad structures andascertaining antiresonant core wall behaviour. Obviously, a morerigorous numerical analysis might involve plotting the proportion oflight in air and F-factor for all values of wavelength within theband-gap for any one given structure, since the plots can vary slightlyat different wavelengths, particularly in the vicinity of modecrossings, as already described.

For the purposes of comparing aspects of the performance of variousdifferent structures it is useful to consider the modes that aresupported in the band gap of various PBG fiber structures. This may beachieved by solving Maxwell's vector wave equation for the fiberstructures, using known techniques. In brief, Maxwell's equations arerecast in wave equation form and solved in a plane wave basis set usinga variational scheme. An outline of the method may be found in Chapter 2of the book “Photonic Crystals—Molding the Flow of Light”, J. D.Joannopoulos et al., ©1995 Princeton University Press.

It can be seen that the performance is different in different regions ofthe plane, that is, for different values of L and W. FIGS. 41 (a) and(b) show examples of lines defining various regions of the L-W planethat are believed to be of particular interest for the structure ofFIG. 1. Other lines in addition to those shown in FIG. 41 may be ofinterest. The structure of FIG. 1 has a pitch of 3.2 μm and is designedfor guiding light centered on the wavelength 1.55 μm; however theresults of FIGS. 39 to 41 are independent of pitch and wavelength (whenboth are scaled congruently) and apply to a broad range of structureshaving the general form of FIG. 1.

In another example of an embodiment of the invention (FIG. 42) awaveguide is provided having a larger core region 110. Core region 110corresponds to 19 unit cells of the cladding structure of the waveguide,whereas core 110 in FIG. 1 corresponds to 7 unit cells. Omission of thering of 12 unit cells results in a different boundary from the boundaryof the waveguide of FIG. 1. The boundary of the FIG. 42 waveguide has 12longer veins 140 and 6 shorter veins (in FIG. 1, there were 6 longerveins 140 and six shorter veins 130). Nodules 165 are provided on eachof the longer veins 140. The nodules are elliptical in form with a majoraxis of length 0.5Λ and a minor axis of length 0.1667Λ. The cladding airfilling fraction is 87.5%. Away from nodules 165, the core wallthickness is 0.055Λ.

The performance of the structure of FIG. 42 is significantly improvedover that of FIG. 1. For the 7-cell structure, best results achievedwere 99.3% light in the low refractive index regions (i.e. air) and anF-factor of 0.1345 Λ⁻¹. For the 19-cell structure, 99.7% of the light isin the low refractive index regions and the F-factor is 0.0636 Λ⁻¹.

Field intensity plots (FIG. 43 (i) and (ii)) show that light in the twoorthogonal polarisation modes ((a) and (b)) guided in the fiber isconcentrated in a single-lobed pattern (resembling the fundamental modeof a standard optical fiber, although the pattern guided in the presentfiber consists of multiple transverse modes). FIG. 43 (iii) shows thedistribution of F-factor, that is, which air-silica boundaries arecontributing most to the F-factor. A bright pixel shows a section ofboundary that is interacting with a high intensity part of the field.The plots demonstrate that there is significant overlap of the light inthe guided mode with the core boundary and illustrate the importance ofnodule dimensions.

Other PBG waveguides having different PBG boundary shapes are shown inFIGS. 44 to 47. In FIG. 44, nodules 4465 are at the mid-points of thelonger veins, as in previously described embodiments, but in this caseare semi-elliptical in shape, being flat on the surface of the veinfurthest from the core and elliptical on the surface of the vein closestto the core. Conversely, in FIG. 45, nodules 4565 are semi-elliptical inshape, being flat on the surface of the vein closest to the core andelliptical on the surface of the vein furthest from the core.

In the embodiment of FIG. 46, the waveguide has a ‘nineteen-cell’ core,as in FIG. 42, but in this case the nodules 4665 are nodes joining pairsof longer veins at their ends and also joining them to other parts ofthe photonic band-gap structure.

In the embodiment of FIG. 47, the waveguide again has a ‘nineteen-cellcore’, but in this case the nodules 4765 are provided form the sixshortest veins in the boundary region.

It will thus be understood that the nodules may take any suitable formand location in the boundary. For example, the nodules need not be atthe mid-point of a vein and may indeed be at a node joining two veins.Furthermore, the nodules need not be elliptical or circular incross-section; they may for example be ‘lumpy’, for example a ‘doublelump’ may be made by fusing two side-by-side rods together duringdrawing of the fiber.

With reference to FIG. 17, fibers such as that of FIG. 1 may be madefrom a preform 1700 comprising a stack of hexagonal capillaries 1705.The hexagonal capillaries 1705 each have a circular bore. The claddingnodes 160 and boundary nodes 150 (from FIG. 1) of the PBG fiberstructure result from the significant volume of glass that is present inthe perform 1700 wherever the corners 1710, 1715 of neighboringcapillaries meet. The nodules 165 are formed from the glass of theinwardly-facing corners 1720 of the capillaries that bound an innerregion 1725 of the pre-form 1700, which is to become the core defectregion 110 of a PBG fiber structure. These corners 1720, and the twosides of each capillary that meet at the corners, recede due to surfacetension as the stack of capillaries is heated and drawn. Such recessionturns the two sides and the corner 1720 into a boundary vein 140, with anodule 165. The inner region 1725 may be formed by omitting the innerseven capillaries from the pre-form and, for example, supporting theouter capillaries using truncated capillaries at either end of thestack, as described in PCT/GB00/01249 (described above) or by etchingaway glass from inner capillaries in accordance with eitherPCT/GB00/01249 or U.S. Pat. No. 6,444,133 mentioned above.

FIG. 48 illustrates one way of arranging a stack of capillaries 1200 tobe drawn into a pre-form and fiber of the kind shown in FIG. 16. Thecladding is formed by stacking round cross section capillaries 1205 in aclose-packed, triangular lattice arrangement. The cladding capillaries1205 have an outer diameter of 1.04 mm and a wall thickness of 40 μm.The inner region 1210 of the stack contains a large diameter capillary1215 having an outer diameter of 4.46 mm and a wall thickness of 40 μm.The large diameter capillary 1215 supports the cladding capillarieswhile the stack is being formed and eventually becomes part of thematerial that forms a core defect boundary 145.

Interstitial voids 1220 that form between each close-packed, triangulargroup of three cladding capillaries are each packed with a glass rod1225, which has an outer diameter of 0.498 mm. The rods 1225 areinserted into the voids 1220 after the capillaries have been stacked.The rods 1225 that are packed in voids 1220 assist in forming claddingnodes 160, which have a diameter that is significantly greater than thethickness of the veins that meet at the nodes. Omission of a rod from avoid in the cladding would lead to the formation of a cladding node thathas a significantly smaller diameter.

In a similar manner, rods 1230 are inserted into voids between thelarge-diameter capillary 1215 and between pairs of capillaries 1205 thatare closest to the large diameter capillary 1215. (The triangularcladding structure naturally divides the innermost ring of capillaries1205 into such pairs.) Rods 1230 are kept in place by thin-walledcapillaries 1239. Smaller gaps 1235 formed within the pairs are notfilled. Rods 1230 form, with silica from surrounding capillaries,nodules 4765 (cf. FIG. 47), while the silica around gaps 1235 formsveins.

The stack 1200 is arranged as described with reference to FIG. 48 and isthen over-clad with a further, relatively thick walled capillary (notshown), which is large enough to contain the stack and, at the sametime, small enough to hold the capillaries and rods in place. The entireover-clad stack is then heated and drawn into a pre-form, during whichtime all the interstitial voids at the boundary, and remaining voidsbetween the glass rods and the cladding capillaries, collapse due tosurface tension. The pre-form is, again, over-clad with a final, thicksilica cladding and is heated and drawn into optical fiber in a knownway. If surface tension alone is insufficient to collapse theinterstitial voids, a vacuum may be applied to the interstitial voids ofthe pre-form, for example according to the process described in WO00/49436 (The University of Bath).

FIGS. 19 and 18 illustrate alternative preform stacks used for makingfibers according to embodiments of the present invention. The stack inFIG. 19 includes a large diameter core capillary replacing sevencladding capillaries. Six rods are fused onto the large diametercapillary; each one coinciding with a point where a cladding capillaryabuts the large diameter capillary. This stack is suitable for making afiber of the kind shown in FIG. 1 or in FIG. 44. The stack in FIG. 18 issimilar to the stack in FIG. 19, apart from the large diameter capillaryreplacing nineteen cladding capillaries and there being twelve rodsattached to the large diameter capillary; each one coinciding with apoint where a cladding capillary abuts the large diameter capillary.This stack is suitable for making a fiber of the kind illustrated inFIG. 42.

In a further alternative way to form the fiber, a graphite insert isprovided as an alternative to large diameter capillary 1215 (of FIG.48). The graphite insert is shaped to be a mould for the desiredboundary shape. During a first drawing step, the stack of capillaries1205 collapses onto the graphite insert and is moulded to its shape. Asthe partly drawn fiber cools, the graphite insert becomes loose and isremoved before a second drawing step, in which the final fiber is drawn.

A further alternative way to form the fiber is by using the processdescribed in PCT/GB00/01249 (described above), wherein the innercapillaries are replaced by truncated capillaries, which support theouter capillaries at either end of the stack. The stack may be drawn toan optical fiber in the normal way, and the parts of the fiberincorporating the truncated capillary material may be discarded. Inprinciple, truncated capillaries may also be used to support the stackpart way along its length.

FIG. 20 a is a photograph, taken by the present inventors through amicroscope, of a rod fused to a large diameter capillary before thecapillary is introduced into a pre-form stack, for example of the kindillustrated in FIG. 19. Whether the rod becomes a bead along a coreboundary (for example as shown in FIG. 1) or a relatively morepronounced nodule protruding only from one side of a core boundary (forexample as shown in FIG. 44) can be controlled by the fiber drawingconditions. For example, hotter drawing conditions under lower tensionpermit a rod and boundary to fuse completely, thereby forming a bead. Incontrast, a colder draw under higher tension prevents complete fusing ofthe rod and core boundary, leaving the rod as a nodule on the surface ofthe core boundary in a final fiber structure. Clearly, a nodule can bearranged to form on an inner or outer periphery of a core boundary,depending on whether the respective rod is positioned on an inner orouter periphery of a large diameter capillary of the pre-form stack. Theproperties of a final fiber structure are expected to vary with beadand/or nodule size and placement.

FIG. 20 b is a SEM image of a bead, magnified by a factor of about 4000,which forms part of a PBG cladding structure according to an embodimentof the present invention. As shown, the bead has formed along arelatively shorter vein of the cladding structure. The structure is aresult of heating and drawing a preform containing the rod shown in FIG.20 a. The drawing conditions included a heating temperature of about2050° C., a draw speed of about 2 ms⁻¹ and a draw tension of about 240g. Clearly, the rod has fused completely with the capillary under thesedrawing conditions. It is expected that cooler and/or faster drawingconditions would lead to the formation of a nodule on the inner surfaceonly of the capillary.

FIG. 49 a is a photograph taken through a microscope of a rod fused tothe outer periphery of a core boundary in a preform stack. In this case,the rod was initially fused inside a cladding capillary and the claddingcapillary was rotated so that the rod was aligned with the point wherethe cladding capillary abutted the large diameter core capillary in thestack. The SEM image in FIG. 49 b shows how the rod becomes a bead alongthe core boundary of a fiber drawn from a preform of the kind shown inFIG. 49 a.

FIG. 32 is a diagram of a transmission system 3200 comprising an opticaltransmitter 3210, an optical receiver 3220 and an optical fiber 3230between the transmitter and receiver. The optical fiber 3230 comprisesalong at least a part of its length an optical fiber according to anembodiment of the present invention. Other components or systems, forexample to compensate for dispersion and loss, would typically beincluded in the system but are not shown in FIG. 32 for the sake ofconvenience only.

The skilled person will appreciate that the various structures describedabove may be manufactured using the described manufacturing process or aprior art processes. For example, rather than using a stacking anddrawing approach to manufacture, a pre-form may be made using a knownextrusion process and then that pre-form may be drawn into an opticalfiber in the normal way.

In addition, the skilled person will appreciate that while the examplesprovided above relate exclusively to PBG fiber cladding structurescomprising triangular arrays, the present invention is in no way limitedto such cladding structures. For example, the invention could relateequally to square lattice structures, or structures that are notclose-packed. In general, the inventors propose that given a claddingstructure that provides a PBG and a core defect in the claddingstructure that supports guided modes, the form of the boundary at theinterface between the core defect and the cladding structure will have asignificant impact on the characteristics of the waveguide, as describedherein.

It will be appreciated that, in practical fibers, it is difficult tocontrol the fabrication process to achieve exact dimensions, forexample, of core boundary nodules. However, the antiresonance minima inF-number (maxima in light in air fraction) are quite broad, comparedwith resonances, which are characterised by sharp peaks at certainthicknesses of core boundary. Thus, a core boundary nodule havingdimensions in the region of an antiresonance minimum, even if notexactly at the minimum, will still provide an advantage over otherwaveguides. It is expected that, as fabrication processes improve, itwill be possible to make a core boundary having nodules having a shapevery close to desired shape. There may be reasons for making a coreboundary nodule which is not optimum according to a strict antiresonanceanalysis. One exemplary reason may be mode crossings, which can havedeleterious effects of the transmission characteristics of a fiber, asdiscussed above.

The distinctive features of the boundary region between the core andcladding regions have been typically described as deformations in theform of enlarged regions, such as beads or nodules on a boundary regionhaving the form of an annular ring. The form of the boundary region mayof course—depending on the frame of reference—just as well be describedin other ways, such as by indentions or by indentations AND enlargedregions.

The skilled person will appreciate that the structures described hereinfit on a continuum comprising a huge number of different structures, forexample having different combinations of core defect size, boundary nodesize, boundary vein thickness and, in general, boundary and claddingform. Clearly, it would be impractical to illustrate each and everyvariant of PBG waveguide structure herein. In particular, wherenumerical values or ranges of values are given herein for a particularparameter, all combinations with values or ranges of values of otherparameters given herein are disclosed unless such combinations are notphysically possible. As such, the skilled person will accept that thepresent invention is limited in scope only by the present claims andequivalents thereof.

1. An elongate waveguide for guiding light comprising: a core comprisingan elongate region of relatively low refractive index; a microstructuredregion around the core comprising elongate regions of relatively lowrefractive index interspersed with elongate regions of relatively highrefractive index; and a boundary at the interface between the core andthe microstructured region, the boundary comprising, in the transversecross-section, a region of relatively high refractive index, which isconnected to the microstructured region at a plurality of nodes, and atleast one relatively enlarged region around the boundary, said enlargedregion having a major dimension and a minor dimension, wherein thelength of the major dimension divided by the length of the minordimension is more than 3.0.
 2. The waveguide according to claim 1,wherein the microstructured region comprises a photonic band-gapstructure.
 3. The waveguide according to claim 2, wherein the boundaryregion has a shape such that, in use, light guided by the waveguide isguided in a transverse mode in which, in the transverse cross-section,more than 95% of the guided light is in the regions of relatively lowrefractive index in the waveguide.
 4. The waveguide as claimed in claim3, in which the boundary region has a shape such that, in use, lightguided by the waveguide is guided in a transverse mode in which, in thetransverse cross-section, more than 50% of the guided light is in theregion of relatively low refractive index in the core.
 5. The waveguideas claimed in claim 3, in which the boundary region has a shape suchthat, in use, light guided by the waveguide is guided in a transversemode providing an F-factor of less than 0.23 μm⁻¹ (0.7 Λ⁻¹).
 6. Thewaveguide as claimed in claim 2, in which the core has, in thetransverse cross-section, an area that is significantly greater than thearea of at least some of the relatively low refractive index regions ofthe photonic bandgap structure, such as, an area that is greater thantwice the area of at least some of the relatively low refractive indexregions of the photonic bandgap structure.
 7. The waveguide as claimedin claim 2, in which the relatively low refractive index regions make upmore than 90% by volume of the photonic bandgap structure.
 8. Thewaveguide as claimed in claim 1, in which the boundary region comprises,in the transverse cross-section, a plurality of relatively highrefractive index boundary veins joined end-to-end around the boundarybetween boundary nodes, each boundary vein being joined between aleading boundary node and a following boundary node, and each boundarynode being joined between two boundary veins and to a relatively highrefractive index region of the microstructured region, and in which atleast one of the boundary veins comprises, along its length or at itsend, an enlarged region that takes the form of a nodule.
 9. Thewaveguide as claimed in claim 8, in which the nodule has a substantiallyelliptical shape in the transverse cross-section, such that an ellipsehaving a major axis of length L and a minor axis of length Wsubstantially fits to the shape of the nodule in the transversecross-section.
 10. The waveguide as claimed in claim 9, in which themajor axis extends along the boundary vein in which the nodule iscomprised.
 11. The waveguide as claimed in claim 9, in which the lengthsW, L of the minor and major axes, respectively, have a mutual relationto each other selected from the group of relations consisting of$W \approx \frac{L}{3}$ and W≧0.238 L.
 12. The waveguide as claimed inclaim 9, arranged to guide light at a wavelength λ₁, which is in theultraviolet, visible or infrared parts of the electromagnetic spectrum.13. The waveguide as claimed in claim 9, arranged to guide light at awavelength λ₂, wherein light guided at the wavelength λ₂ exhibits lowerloss than light guided in the waveguide at any other wavelength.
 14. Thewaveguide as claimed in claim 12, there being a parameter X that isequal to the wavelength λ₁ in which the mutual relationships betweenparameters W, L, X are selected from the group of relationshipsconsisting of${L \geq \frac{5\; X}{12}},{L \approx \frac{X}{2}},{L \leq \frac{7\; X}{12}},{W > \frac{X}{18}},{W > \frac{5\; X}{36}},{W \approx \frac{X}{6}},{{\begin{matrix}{{W \leq \frac{7\; X}{36}},} & {{{L \times W} \geq {0.058\; X^{2}}},}\end{matrix}L \times W} \approx \frac{X^{2}}{12}},{{L \times W} \leq {0.113\; X^{2}}},{W \leq {( {\frac{1}{18} + \frac{L}{3}} )X}},{W \geq {( {{- \frac{1}{18}} + \frac{L}{3}} )X}},{W \geq {( {\frac{5}{18} - \frac{L}{3}} )X}},{W \leq {( {\frac{7}{18} - \frac{L}{3}} )X}},{W \geq {( {{- 0.133} + {0.467\; L}} )X}},{W \leq {( {0.095 + {0.238\; L}} )X}},{W \geq {( {0.333 - {0.467\; L}} )X}},{W \leq {( {0.333 - {0.238\; L}} )X}},{W \leq {( {0.467 - {0.467\; L}} )X}},{W \leq {( {0.238 - {0.238\; L}} ){X.}}}$15. The waveguide as claimed in claim 9, wherein the microstructuredregion may comprise a substantially periodic array of elementscharacterized by a unit cell and a pitch Λ, there being a parameter Xthat is equal to the pitch Λ in which the mutual relationships betweenparameters W, L, X are selected from the group of relationshipsconsisting of${L \geq \frac{5\; X}{12}},{L \approx \frac{X}{2}},{L \leq \frac{7\; X}{12}},{W > \frac{X}{18}},{W > \frac{5\; X}{36}},{W \approx \frac{X}{6}},{{\begin{matrix}{{W \leq \frac{7\; X}{36}},} & {{{L \times W} \geq {0.058\; X^{2}}},}\end{matrix}L \times W} \approx \frac{X^{2}}{12}},{{L \times W} \leq {0.113\; X^{2}}},{W \leq {( {\frac{1}{18} + \frac{L}{3}} )X}},{W \geq {( {{- \frac{1}{18}} + \frac{L}{3}} )X}},{W \geq {( {\frac{5}{18} - \frac{L}{3}} )X}},{W \leq {( {\frac{7}{18} - \frac{L}{3}} )X}},{W \geq {( {{- 0.133} + {0.467\; L}} )X}},{W \leq {( {0.095 + {0.238\; L}} )X}},{W \geq {( {0.333 - {0.467\; L}} )X}},{W \leq {( {0.333 - {0.238\; L}} )X}},{W \leq {( {0.467 - {0.467\; L}} )X}},{W \leq {( {0.238 - {0.238\; L}} ){X.}}}$16. The waveguide as claimed in claim 13, there being a parameter X thatis equal to the wavelength λ₂ in which the mutual relationships betweenparameters W, L, X are selected from the group of relationshipsconsisting of${L \geq \frac{5\; X}{12}},{L \approx \frac{X}{2}},{L \leq \frac{7\; X}{12}},{W > \frac{X}{18}},{W > \frac{5\; X}{36}},{W \approx \frac{X}{6}},{{\begin{matrix}{{W \leq \frac{7\; X}{36}},} & {{{L \times W} \geq {0.058\; X^{2}}},}\end{matrix}L \times W} \approx \frac{X^{2}}{12}},{{L \times W} \leq {0.113\; X^{2}}},{W \leq {( {\frac{1}{18} + \frac{L}{3}} )X}},{W \geq {( {{- \frac{1}{18}} + \frac{L}{3}} )X}},{W \geq {( {\frac{5}{18} - \frac{L}{3}} )X}},{W \leq {( {\frac{7}{18} - \frac{L}{3}} )X}},{W \geq {( {{- 0.133} + {0.467\; L}} )X}},{W \leq {( {0.095 + {0.238\; L}} )X}},{W \geq {( {0.333 - {0.467\; L}} )X}},{W \leq {( {0.333 - {0.238\; L}} )X}},{W \leq {( {0.467 - {0.467\; L}} )X}},{W \leq {( {0.238 - {0.238\; L}} ){X.}}}$17. The waveguide according to claim 1, wherein there are more than sixenlarged regions around the boundary, such as twelve or more enlargedregions around the boundary, such as eighteen enlarged regions aroundthe boundary.
 18. The waveguide according to claim 8, wherein aplurality of enlarged regions are positioned along veins and spacedapart from any nodes.
 19. The waveguide according to claim 8, wherein anenlarged region comprises a relatively thick vein, compared to thethickness of at least one other vein, extending between a pair ofneighboring nodes.
 20. The waveguide according to claim 8, wherein anenlarged region is coincident with a node such that the node has anuncharacteristic form relative to the photonic band-gap cladding. 21.The waveguide according to claim 8, wherein said nodule has a majordimension and the length of the major dimension is at least 0.42 timesthe distance between the two adjacent nodes on either side of theenlarged region and the length of the major dimension is less than 0.98times the distance between the two adjacent nodes.
 22. The waveguideaccording to claim 1, wherein the boundary has no more than two foldrotational symmetry about any longitudinal axis thereof at least in partby virtue of the presence or placement of the or each relativelyenlarged region.
 23. The waveguide according to claim 22, wherein theboundary has only two fold rotational symmetry.
 24. A preform for amicrostructured optical fiber waveguide, comprising a stack of parallel,first elongate elements supported, in the plane cross section, around aninner region, which is to become a relatively low refractive index coreregion when the preform is drawn into a fiber, the preform furthercomprising second elongate elements, also supported or situated aroundthe inner region, said second elements being arranged to generate a coreboundary, at the interface between the photonic band-gap cladding andthe core, when the preform is drawn into fiber, the arrangement ofsecond elements being such that the core boundary comprises at least onerelatively enlarged region when the preform is drawn into fiber.
 25. Aphotonic crystal fiber comprising: an outer structure comprising aperiodic array of unit cells, each unit cell comprising a central regionof a vacuum or a fluid and an outer region of a solid material, theperiodic array having a pitch Λ; and a core, comprising an elongateregion of a vacuum or a fluid; the outer structure including a boundaryregion comprising a plurality of veins of relatively high refractiveindex that surrounds, in a transverse cross-section of the waveguide,the core; wherein the veins include nodules that are antiresonant at awavelength of light guided in the waveguide.